This blog is the online extension of our intermediate classrooms. Our goal is to enhance and document our learning experience throughout the school year, and share this journey with teachers, parents and students. We welcome your constructive feedback, and we look forward to learning with you!
Math: 70@180=110 = ACD =110 left ac =cd = angle @a = angle @d cdb=cbd=110 divided by 2 = 55 = acd=cda=70 divided into 2=35 degrees cd block angle measurement rel. to adb, so add angles rel. to it cda=35 cdb=55 35 + 55 =90 =right angle = 90 degrees sol. Now the explanation of what I've done. First, it states bcd is 70 degrees, and as A to B is 180 degrees relative to C, so I subtracted 70 from 180. this got me 110 degrees. The text also states ac, cb, and cd are all the same length, and as all of the even angles on the shape are connected to C, and the angle of C relative to b and d is stated, which are the same length, the only possible way to make a working triangle with these variables is to divide the remainder (Relative to 180, the total angle of all triangles) by the amount of angles, which is 2. This got me 35 degrees for both angles. I then noticed that 35 degrees is relative to angles C and B, not A, and B. When I look at the image, the line cd is blocking the angle from being adb. From that, I know that I need to know the angle of the other side and combine them to get the actual angle of adb. I divided the angle from 180 degrees (-70), which can get me the angles as ac is also the same and protruding from C as cb, and cd. The angle of acd was 110 degrees as ab is a 180 degree line, so if it wasn't for the angle that made 180 degrees relative to C's angle, then there would be no need to subtract the angle of the other side. Dividing 110 (180 - 70) by the amount of angles gotten me 55. So angles of D are calculated on both sides, so the answer relative to ad and bd is combined to be able to calculate adb, which is 35 +55, which is 90 degrees
To find the angle D, I first looked at the picture and made a list of things I knew: - Angle BCD is 70° -Triangle BCD is isosceles -C-D, B-C, and A-C are all the same length
Because I knew that triangle BCD is isosceles, that means that angle B and angle D are the same degrees. I also knew that all the angles in a triangle is equal to 180°. So 180° - 70° = 110° ÷ 2 = 55° for each angle in BCD (triangle).
A straight line is 180°, so the angles of A and C should add up to 180°. 180° - 70° = 110°, so the other side of angle C is 110°.
180° - 110° = 70° ÷ 2 = 45° for angle D and angle A (because it’s an isosceles triangle). So the two angles of angle D added is the angle of D
Okay, completely wrong answer. 70° ÷ 2 = 35°, and 55° + 35° = 90°, and Angle D is 90° (This is the result of not checking my work, then double-checking, and finding out that I was wrong, and then triple-checking and finding out I was still wrong)
Angle D or Angle ADB is 90°. If found this out by using the info given regarding angles and side lengths. I know that since Triangle BCD is isosceles, the other two angles will be the same. So 180=70 +110 110÷2= 55°. Then, knowing that one part of Angle D is 55°, I can work on the next triangle. I know that for the other angle in the other triangle for Angle D is 110° as 180 (straight line)-70° already given= 110° Then, I find that this triangle is also isosceles, so the next two angles will be the same. 180°-110°=70° divided by 2= 35° Adding 35° to 55° from the other triangle gives me the full angle for D, which is 90°.
The answer is Angle ADB is 90°. After reading it, there are a list of things you can determine or are given. AC=CB=CD means that triangles ACD and BCD are both isosceles. Angle B and BDC are equal Angle A and CDA are equal A triangle's angles add up to 180°.
Ok now that that knowledge we can start. 180-70=110 110/2=55 Angle B and BDC are both 55°. We now have half of angle D determined.
Now angle ACD is 110° because, ACD + BCD need to equal a straight angle. This means that since Angle A and CDA are equal 180-110=2A/2CDA A or CDA= 35°
The other half of D is determined. 35° + 55° = 90° So the final answer is, Angle D is 90° .
The question states that angle BCD is 70°, lines AC, CB, and CD are all the same. Also, from background knowledge I know that the triangle is isosceles so, angles B and D must have the same °. We all know that all the angles of a triangle add up to 180°, so 180-70=110° and there are two smaller triangles inside triangle ABCD so, 110÷2=55°. I also know that a straight line is a straight angle which is 180 so angle ACB is 180°-110=70, 70 ÷ 2 =35°. In conclusion, 35+55=90°. I found this potw a bit challenging, as I had to seek help from another family member.
The measure of ADB is 90 degrees. What I did was create my own version of the triangle and I started with BD. I simply created a regualar straight line so I could make triangle BCD. I know that angle BCD is 70 degrees and triangle BCD is an isosceles triangle (meaning two sides are equal), and I also know that all the angles in a triangle add up to 180 degrees. This meant I had to subtract 70 from 180 and divide the number left to find out the angles of the equal sides. I got 55 so that meant angles DBC and BDC are 55 degrees. Now I have triangle BCD and I still had to measure angle ADB. Since the length of side AC are equal to side BC and DC, I made side AC the same length as them. Now I just connected point D to point A completing the full triangle. Finally, I measured angle ADB which was 90 degrees.
Here's how I answered the question: So the questions said that AC=CB=CD would mean that triangle BCD is isosceles which means 2 angles are the same measurements and since angle BCD is 70 degrees angle CDB should be half of the remaining degrees. Since a triangle's angles add up to be 180 degrees in total angle ADB should be half of the remaining degrees since the triangle has two equal angles. 180 -70 equals 110 divided by half is 55 degrees so angle CDB is 55 degrees. That’s only half of the triangle so since angle BCD is 70 degrees and a straight line is 180 degrees angle ACD is 110 degrees because 110 + 70 is 180. Plus since AC=CB=CD that means triangle ACD is also an isosceles triangle which means angle CAD and CDA should be the same so 180-110 equals 70 divided by 2 to get the angle of ADC equals 35 so angle ADC is 35 which is part of what angle ADB is and when adding the angles together ( ADC and CDB) you get 90 degrees. Angle ADB is 90 degrees.
In order to answer this question I first wrote down what I already knew -AC=CB=CD -angle BCD is 70 degrees -In addition the triangle BCD is an isosceles since it is isosceles i decided to start by finding the angles of B and part of D. 180-70=110. Then 110/2=55. Therefore part of angle D is 55 degrees. Then since angle BCD is 70 degrees on one side then it is 110 degrees on the other since it is a straight line. Then you would do 180-110 to get 70 degrees. 70/2=35. Finally, 35+55=90. Therefore angle D is 90 degrees.
The way I got my answer is: Since a triangles interior angle equals 180 total so its 180-70, which equals 110. Then you take 110 and divide it by 2, because on an isosceles triangle two of the angles are the same, = 65. so if one correctly.its 180-70= 110, 110 divided by 2= 65. 55+55+70=180. Angle BCA is 180 because its a straight angle and 180-110, i chose 110 because it was the number leftover after i subtracted 180-70, and got 70 (the sum of the two bottom angles) then i divided it by two to find out each individual angles, 35. 35+55 is 90
I didn't really need to look too far into the question because the angle was clearly a right angle in the picture. Therefore, the angle is clearly 90 degrees.
All angles combined in a triangle would 180 degrees because on a square there is all right angles which is 90*4 = 360. So a triangle is half making it 180 degrees. So than I subtracted what was given of 70 degrees and got 110 degrees. Now since triangle BCD was a isosceles triangle 2 of the sides would be the same. So now I had to divide 110 into 2 getting 55 degrees. So now that the angle C is to be divided by two to get the answer. 70 divided into 2 equals 35. Then the 35 is added to 55 to get the answer of 90 degrees. Another way I did it was looking at the triangle and seeing that angle d was a right angle making it 90 degrees. Then that would make the angle A 35 degrees. So to double check adding them all up: 35 + 55 + 90 = 180
Angle ABD is 90 degrees. How I solved the question: I know that a triangle should equal to 180 degrees, the triangle was an isosceles, and that angle BCD was 70 degrees.
That would mean the 2/3 lengths of the triangle were the same, meaning 1 side length was different.
180 - 70 = 110 l l triangle one full angle side
With 110, you would need to divide it by 2, due to the equal isosceles triangle lengths.
110 ÷ 2 = 55 < angle of the two sides
If BCD is 70 degrees on one side, then it is 110 degrees on the other since it is a straight adding up to 180. 180 - 110 = 70. Half of 70 is 35. Since 35 plus 55 is 90, the angle D = 90 degrees
The angle ABD is 90 degrees. How I figured this out was since that both triangles were isosceles triangles from where it stated AC=CB=CD. Since angle BCD is 70 degrees and the triangle is an isosceles, I did 180-70 to get 110. I did 180 because all angles in a triangle must add up to 180. So, 110 is angles B and part of D added up so I have to divide it by 2 which gives me 55. Then I know that angle BCD is 70 degrees making it 110 on the other side to make it a straight line. To find the rest of the angles you would do 180-110 to get 70. Then you divide 70 by 2 to get the other angles which was 35. Then you add up the angles of the 2 triangles, 35+55 to get 90 degrees.
In triangle BCD, the lines through the sides show me that triangle BCD is isosceles, and that the remaining two angles in BCD would have to be equal. Thinking ? + ? + 70 = 180 (because all the angle sin a triangle have to equal 180 degrees when added up). in my equation, the unknowns would have to equal to each other as isosceles triangles have two equal angles.
? + ? + 70 = 180 2? = 180 - 70 2? = 110 ? = 55
Therefore, in both triangle ABD and triangle BCD, angle B equals 55. I also know that 55 is part of angle D
Next, I try to find the measure of the other side of the angle c. Since it’s on a straight line, and part of it is 70 degrees, the other side would be there rest of the degrees needed to get from 70 to 180 (the measure of a straight line). 180-70= 110.
Therefore, in triangle ACD, C= 110. Knowing this can help me find the measure of angle D in this triangle, which is also the other part of angle D in the triangle ADB.
110 + 2? = 180 2? = 180-110 2? = 70 ? = 35
Therefore the other part of angle D, besides 55 degrees must be 35 degrees. Adding them to find the total measure of angle D:
55 + 35 = 90
Therefore Angle D is 90 degrees, Angle A is 35 degrees, and angle C is 55 degrees.
I didn't exactly do math, which was kind of cheating, but I used logic instead. You told me to find angle D. If you look in the picture, you can see very clearly a right angle is D. I know that a right angle is equal to 90 degrees, therefore angle D is 90 degrees.
To find out what angle BDC was I had to subtract 70 from 180 to get 110. Then I Divided 110 into 2 to 55, so angle BDC is 55 degrees. Then if It is 70 on one side then it is 110 on the other side for them to add up to 180. Now that I know that ACD is 110 degrees, I'll divide 70 into 2 and add it to 55. 70/2=35 35+55= 90 ADB is a right (90 degrees) angle.
I really liked the full explanations for what seemed to be an easier than usual question. Great job in getting the correct response of 90 degree for the angle. Remember, do not just assume it is 90 degree because "it looks like it", you must validate and justify opinions in math.
I actually didn't use the math approach, I just saw that the angle pretty much looks like a right angle (90 degrees) so I concluded that angle D is a 90 degree angle.
Math:
ReplyDelete70@180=110 = ACD
=110 left
ac =cd = angle @a = angle @d
cdb=cbd=110 divided by 2 = 55 =
acd=cda=70 divided into 2=35 degrees
cd block angle measurement rel. to adb, so add angles rel. to it
cda=35 cdb=55
35 + 55 =90 =right angle
= 90 degrees sol.
Now the explanation of what I've done.
First, it states bcd is 70 degrees, and as A to B is 180 degrees relative to C, so I subtracted 70 from 180.
this got me 110 degrees. The text also states ac, cb, and cd are all the same length, and as all of the even angles on the shape are connected to C, and the angle of C relative to b and d is stated, which are the same length, the only possible way to make a working triangle with these variables is to divide the remainder (Relative to 180, the total angle of all triangles) by the amount of angles, which is 2. This got me 35 degrees for both angles. I then noticed that 35 degrees is relative to angles C and B, not A, and B. When I look at the image, the line cd is blocking the angle from being adb. From that, I know that I need to know the angle of the other side and combine them to get the actual angle of adb. I divided the angle from 180 degrees (-70), which can get me the angles as ac is also the same and protruding from C as cb, and cd. The angle of acd was 110 degrees as ab is a 180 degree line, so if it wasn't for the angle that made 180 degrees relative to C's angle, then there would be no need to subtract the angle of the other side. Dividing 110 (180 - 70) by the amount of angles gotten me 55. So angles of D are calculated on both sides, so the answer relative to ad and bd is combined to be able to calculate adb, which is 35 +55, which is 90 degrees
To find the angle D, I first looked at the picture and made a list of things I knew:
ReplyDelete- Angle BCD is 70°
-Triangle BCD is isosceles
-C-D, B-C, and A-C are all the same length
Because I knew that triangle BCD is isosceles, that means that angle B and angle D are the same degrees. I also knew that all the angles in a triangle is equal to 180°. So 180° - 70° = 110° ÷ 2 = 55° for each angle in BCD (triangle).
A straight line is 180°, so the angles of A and C should add up to 180°.
180° - 70° = 110°, so the other side of angle C is 110°.
180° - 110° = 70° ÷ 2 = 45° for angle D and angle A (because it’s an isosceles triangle). So the two angles of angle D added is the angle of D
45° + 55° = 95°
Angle D is 95°.
Oops, typos, I meant 45° + 55° = 100°
DeleteOkay, completely wrong answer.
Delete70° ÷ 2 = 35°, and 55° + 35° = 90°, and Angle D is 90° (This is the result of not checking my work, then double-checking, and finding out that I was wrong, and then triple-checking and finding out I was still wrong)
Angle D or Angle ADB is 90°. If found this out by using the info given regarding angles and side lengths.
ReplyDeleteI know that since Triangle BCD is isosceles, the other two angles will be the same.
So 180=70 +110
110÷2= 55°.
Then, knowing that one part of Angle D is 55°, I can work on the next triangle.
I know that for the other angle in the other triangle for Angle D is 110° as 180 (straight line)-70° already given= 110°
Then, I find that this triangle is also isosceles, so the next two angles will be the same.
180°-110°=70° divided by 2= 35°
Adding 35° to 55° from the other triangle gives me the full angle for D, which is 90°.
The answer is Angle ADB is 90°.
ReplyDeleteAfter reading it, there are a list of things you can determine or are given.
AC=CB=CD means that triangles ACD and BCD are both isosceles.
Angle B and BDC are equal
Angle A and CDA are equal
A triangle's angles add up to 180°.
Ok now that that knowledge we can start.
180-70=110
110/2=55
Angle B and BDC are both 55°.
We now have half of angle D determined.
Now angle ACD is 110° because, ACD + BCD need to equal a straight angle.
This means that since Angle A and CDA are equal 180-110=2A/2CDA
A or CDA= 35°
The other half of D is determined.
35° + 55° = 90°
So the final answer is, Angle D is 90° .
The question states that angle BCD is 70°, lines AC, CB, and CD are all the same. Also, from background knowledge I know that the triangle is isosceles so, angles B and D must have the same °. We all know that all the angles of a triangle add up to 180°, so 180-70=110° and there are two smaller triangles inside triangle ABCD so, 110÷2=55°. I also know that a straight line is a straight angle which is 180 so angle ACB is 180°-110=70, 70 ÷ 2 =35°.
ReplyDeleteIn conclusion, 35+55=90°.
I found this potw a bit challenging, as I had to seek help from another family member.
The measure of ADB is 90 degrees.
ReplyDeleteWhat I did was create my own version of the triangle and I started with BD. I simply created a regualar straight line so I could make triangle BCD. I know that angle BCD is 70 degrees and triangle BCD is an isosceles triangle (meaning two sides are equal), and I also know that all the angles in a triangle add up to 180 degrees. This meant I had to subtract 70 from 180 and divide the number left to find out the angles of the equal sides. I got 55 so that meant angles DBC and BDC are 55 degrees. Now I have triangle BCD and I still had to measure angle ADB. Since the length of side AC are equal to side BC and DC, I made side AC the same length as them. Now I just connected point D to point A completing the full triangle. Finally, I measured angle ADB which was 90 degrees.
This comment has been removed by the author.
ReplyDeleteHere's how I answered the question:
ReplyDeleteSo the questions said that AC=CB=CD would mean that triangle BCD is isosceles which means 2 angles are the same measurements and since angle BCD is 70 degrees angle CDB should be half of the remaining degrees. Since a triangle's angles add up to be 180 degrees in total angle ADB should be half of the remaining degrees since the triangle has two equal angles. 180 -70 equals 110 divided by half is 55 degrees so angle CDB is 55 degrees. That’s only half of the triangle so since angle BCD is 70 degrees and a straight line is 180 degrees angle ACD is 110 degrees because 110 + 70 is 180. Plus since AC=CB=CD that means triangle ACD is also an isosceles triangle which means angle CAD and CDA should be the same so 180-110 equals 70 divided by 2 to get the angle of ADC equals 35 so angle ADC is 35 which is part of what angle ADB is and when adding the angles together ( ADC and CDB) you get 90 degrees.
Angle ADB is 90 degrees.
In order to answer this question I first wrote down what I already knew
ReplyDelete-AC=CB=CD
-angle BCD is 70 degrees
-In addition the triangle BCD is an isosceles
since it is isosceles i decided to start by finding the angles of B and part of D. 180-70=110. Then 110/2=55. Therefore part of angle D is 55 degrees. Then since angle BCD is 70 degrees on one side then it is 110 degrees on the other since it is a straight line. Then you would do 180-110 to get 70 degrees. 70/2=35. Finally, 35+55=90. Therefore angle D is 90 degrees.
The way I got my answer is:
ReplyDeleteSince a triangles interior angle equals 180 total so its 180-70, which equals 110. Then you take 110 and divide it by 2, because on an isosceles triangle two of the angles are the same, = 65.
so if one correctly.its 180-70= 110, 110 divided by 2= 65. 55+55+70=180.
Angle BCA is 180 because its a straight angle and 180-110, i chose 110 because it was the number leftover after i subtracted 180-70, and got 70 (the sum of the two bottom angles) then i divided it by two to find out each individual angles, 35. 35+55 is 90
I didn't really need to look too far into the question because the angle was clearly a right angle in the picture. Therefore, the angle is clearly 90 degrees.
ReplyDeletes
ReplyDeleteAll angles combined in a triangle would 180 degrees because on a square there is all right angles which is 90*4 = 360. So a triangle is half making it 180 degrees. So than I subtracted what was given of 70 degrees and got 110 degrees. Now since triangle BCD was a isosceles triangle 2 of the sides would be the same. So now I had to divide 110 into 2 getting 55 degrees. So now that the angle C is to be divided by two to get the answer. 70 divided into 2 equals 35. Then the 35 is added to 55 to get the answer of 90 degrees. Another way I did it was looking at the triangle and seeing that angle d was a right angle making it 90 degrees. Then that would make the angle A 35 degrees. So to double check adding them all up: 35 + 55 + 90 = 180
ReplyDeleteAngle ABD is 90 degrees.
ReplyDeleteHow I solved the question:
I know that a triangle should equal to 180 degrees, the triangle was an isosceles, and that angle BCD was 70 degrees.
That would mean the 2/3 lengths of the triangle were the same, meaning 1 side length was different.
180 - 70 = 110
l l
triangle one
full angle side
With 110, you would need to divide it by 2, due to the equal isosceles triangle lengths.
110 ÷ 2 = 55 < angle of the two sides
If BCD is 70 degrees on one side, then it is 110 degrees on the other since it is a straight adding up to 180.
180 - 110 = 70. Half of 70 is 35. Since 35 plus 55 is 90, the angle D = 90 degrees
The angle ABD is 90 degrees.
ReplyDeleteHow I figured this out was since that both triangles were isosceles triangles from where it stated AC=CB=CD. Since angle BCD is 70 degrees and the triangle is an isosceles, I did 180-70 to get 110. I did 180 because all angles in a triangle must add up to 180. So, 110 is angles B and part of D added up so I have to divide it by 2 which gives me 55. Then I know that angle BCD is 70 degrees making it 110 on the other side to make it a straight line. To find the rest of the angles you would do 180-110 to get 70. Then you divide 70 by 2 to get the other angles which was 35. Then you add up the angles of the 2 triangles, 35+55 to get 90 degrees.
In triangle BCD, the lines through the sides show me that triangle BCD is isosceles, and that the remaining two angles in BCD would have to be equal. Thinking ? + ? + 70 = 180 (because all the angle sin a triangle have to equal 180 degrees when added up). in my equation, the unknowns would have to equal to each other as isosceles triangles have two equal angles.
ReplyDelete? + ? + 70 = 180
2? = 180 - 70
2? = 110
? = 55
Therefore, in both triangle ABD and triangle BCD, angle B equals 55. I also know that 55 is part of angle D
Next, I try to find the measure of the other side of the angle c. Since it’s on a straight line, and part of it is 70 degrees, the other side would be there rest of the degrees needed to get from 70 to 180 (the measure of a straight line). 180-70= 110.
Therefore, in triangle ACD, C= 110. Knowing this can help me find the measure of angle D in this triangle, which is also the other part of angle D in the triangle ADB.
110 + 2? = 180
2? = 180-110
2? = 70
? = 35
Therefore the other part of angle D, besides 55 degrees must be 35 degrees. Adding them to find the total measure of angle D:
55 + 35 = 90
Therefore Angle D is 90 degrees, Angle A is 35 degrees, and angle C is 55 degrees.
To verify:
A+C+D=180
90+55+35+ 180
90+90=180
I didn't exactly do math, which was kind of cheating, but I used logic instead. You told me to find angle D. If you look in the picture, you can see very clearly a right angle is D. I know that a right angle is equal to 90 degrees, therefore angle D is 90 degrees.
ReplyDeleteTo find out what angle BDC was I had to subtract 70 from 180 to get 110. Then I Divided 110 into 2 to 55, so angle BDC is 55 degrees. Then if It is 70 on one side then it is 110 on the other side for them to add up to 180. Now that I know that ACD is 110 degrees, I'll divide 70 into 2 and add it to 55.
ReplyDelete70/2=35
35+55= 90
ADB is a right (90 degrees) angle.
I really liked the full explanations for what seemed to be an easier than usual question. Great job in getting the correct response of 90 degree for the angle. Remember, do not just assume it is 90 degree because "it looks like it", you must validate and justify opinions in math.
ReplyDeleteI actually didn't use the math approach, I just saw that the angle pretty much looks like a right angle (90 degrees) so I concluded that angle D is a 90 degree angle.
ReplyDeleteI see that Jessica did the same thing... Wow!
ReplyDelete