Can somone help me with this 1 problem? QRST is a parallelogram. Determine the measure of ∠Q

1 answer:

3 0

(In the picture, QRST looks like a rhombus, so I will assume that it is a rhombus.)

In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.)

We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62

I got m<Q = 62 degrees. Hope this helps!

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