POTW Gr. 8 Answer:
POTW Gr. 7 Answer:
POTW #21 Gr. 8 Question:
POTW #21 Gr. 7 Question:
Thursday, February 16, 2017
POTW #21 - Geometry Minds-On!
Hopefully you got some cents (get it?) from last week's problem. Please work through the latest POTW below. Our next unit after algebra is in geometry, which the latest POTW investigates!
POTW Gr. 8 Answer:
POTW Gr. 7 Answer:
POTW #21 Gr. 8 Question:
POTW #21 Gr. 7 Question:
POTW Gr. 8 Answer:
POTW Gr. 7 Answer:
POTW #21 Gr. 8 Question:
POTW #21 Gr. 7 Question:
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How I did it was to figure out Angle PMQ first, because we have enough information.
ReplyDeleteAngle JML is 90 degrees, since the shape is a square, and Angle PMJ and QML are both 60 degrees since the triangles are equilateral.
The total degrees of the 4 angles is 360, so I simply subtract:
360-90-60-60=150 degrees. The angle PMQ is 150 degrees.
Since the total amount of degrees in Triangle MPQ is 180, Angle QPM and MPQ is 180-150=30 degrees. However, because both of these angles are the same since they are made from a congruent equilateral triangle, I can divide by 2, which gives me 15 degrees.
Angle MPQ is 15 degrees.
I really don't know if this is right, as there was some assuming in the end, but I couldn't really see where to figure it out, so oh well!
-Alan
I think the answer is that angle MPQ is equal to 30 degrees. Now since the triangles JMP and MLQ are both equilateral all of there angles are equal to 60 degrees. Angle PMQ is a mix of two 60 degree angles so it is 120 degrees. That leaves another 60 degrees for the other two angles in triangle PMQ. Since both of them are connected to the same equilateral triangles they are both the same so the remaining 60 degrees are divided into two to be 30 degrees.
ReplyDeleteFirst, what i did was figure out how many degrees angles PMJ and QML were. These were the two closest 2 angles to PMQ. Also since we know that there were two congruent triangles that were equilateral, that means all 3 of the angles equal 60 degrees. Angle PMJ and QML equal 60 degrees, meaning that angle PMQ equals 120 degrees. And since we know that a triangle has to equal up to 180 degrees, this means that the other two angles have to be 60 degrees, and since there are two of them, then we divide by 2 and get 30 degrees.
ReplyDelete120 30 and 30 are all three angles
I am not exactly sure if this is correct, as i didnt' really understand how to do this question otherwise so may be incorrect
DeleteGrade 7 POTW:
ReplyDeleteFirst I needed to figure out some of the other angles before we can find angle MPQ.
So, I knew that JML is 90 degrees, since it was part of a square. Next, I knew that angles PMJ and LMQ were the 60 degrees because it is an equilateral triangle.
So, in order to find what the angle MPQ is, we need to first find the angle PMQ. Since the total of the 4 angles must be equaled to 360 degrees, we need to add up all the angles we knew and subtract it by 360. So we would do:
60+60+90=210
360-210=150
So now we know that angle PMQ is 150 degrees. So to find angle MPQ, we would subtract 180 by 150, because that is the total degrees of a triangle. That means that the other two angles in that triangle is equaled to 30 degrees. And now to find angle MPQ, we would divide 30 by 2, leaving us with 15.
Therefore, angle MPQ is equaled to 15 degrees.
Here's how I went about solving the Grade 7 POTW:
ReplyDeleteWe know that triangles "PJM" and "MLQ" are equilateral which means that each corner is equal to 60 degrees. The angle of "M" on both triangles would be equal to 60 degrees which means that we do 60 * 2 to get 120. This means that the angle of "M" on triangle "MPQ" is 120 degrees. As for the two remaining angles, we know that they are both connected to an equilateral triangle. That means that they would be the same in degrees. A triangle has a total of 180 degrees, and that would mean we could do 180 - 120 to get 60. Then 60 / 2 to give us a quotient of 30. Therefore the degrees values of triangle "MPQ" are: M = 120 degrees, P = 30 degrees, and Q = 30 degrees.
Her's how to solve the question is that since an equilateral triangle's angles are always 60 degrees. 60*2=120 so the angle at M is 120 degrees. Since a triangles angles always add up to 180 degrees and this is a isosceles triangle the other 2 angles are equal. 180-120=60. 60/2=30 so angles P and Q are both 30 degrees.
ReplyDeleteGrade 7: I know triangles have a total degrees of 180. With the angle being a square the are 360 degrees in this. PJM=60 MQL=60 Square=90. 360-210=150
ReplyDeleteThe angles of the unknown triangle are: 150,15,15 which is 150.
I solved this problem in my math book. I got the answer Angle BAD = 100 degrees.
ReplyDeleteGrade 7 POTW
ReplyDeleteBecause the triangles are all equilateral, each angle is 60 degrees. Since angle M is made out of two triangles with 60 degree sides, angle M must equal 120 degrees.
A triangle's angles' degrees always equal 180 degrees, so 60 degrees must be divided between P and Q. Because the two equilateral triangles are perfectly aligned with a square, which has all sides equal, each triangle must be an exact replica of the other, meaning the 60 degrees must be divided equally, so angle P and Q each measure 30 degrees.
Therefore, angle P and Q measure 30 degrees each, and angle M measures 120 degrees.
Angle MPQ is 15 degrees.
ReplyDeleteTo solve this, I first looked at all the information we had. I know that all angles of a square are 90 degrees and all 3 angles of a triangle has to add up to 180 degrees and equilateral triangles all have 60 degree angles . I mainly focused on the 360 angle where angle M was. 360 degrees - 90 degrees - (60 degrees * 2) = 150. Angle PMQ equals 150. Now all I need to do is subtract 150 from 180 and divide the difference by 2 since there are still two unknown angles that are the same. (180-150)/2=15.
Therefore, angle MPQ is 15 degrees.
Grade 7 POTW:
ReplyDeleteI knew all the angles of the square were 90 degrees and the equilateral triangles have an angle 60 degrees. I focused on getting angle m, the surrounding angles were as follows: 90, 60, 60. If I add all of them together, I receive 210. So I subtract 210 by 360 and get 150. From there I subtract 150 from 180, since I triangle has 180 degrees and it equals 30. And since there are 2 angles that are the same, I divide 30 by 2, which ends up as angle MPQ is 15 degrees.
Grade 7 POTW
ReplyDeleteI looked at M as a 360 degree angle and subtracted the parts that were not a part of PMQ from 360.
Those parts include: PMJ, JML, LMQ
I know that JML is a part of a square so it must be 90 and that PMJ and LMQ are a part of a equilateral triangle so they must be 60 degrees.
360 - 90 - 60 - 60 = 150.
To find angle MPQ, I must subtract the others angles from 180 (the sum of the interior triangles). I already know PMQ (150) so 180 - 150 = 30. The sum of the other two triangles is 30. Since they are both made from congruent triangles, the triangle must be isosceles. That means the angles are equal.
30 /2 = 15.
Angle MPQ is 15 degrees.