In Parallelogram ABCD, m ∠ A = ( 7 y + 13 ) ° m ∠ B = ( 106 − 2 x ) ° m ∠ C = ( 10 y − 32 ) ° m ∠ D = ( 3 x − 4 ) ° What are the values of x and y?

Question

show all work and explain in Use words, numbers, and/or equations to explain your work.

Answer 1

In a parallelogram opposite angles are equal. Therefore angles A and C are equal and B and D are equal.

So 7y+13=10y-32, 106-2x=3x-4.

In the first equation subtract 7y from each side: 13=3y-32, now add 32 to each side: 45=3y. Divide through by 3: 15=y, so y=15.

In the second equation add 2x to each side: 106=5x-4, now add 4 to each side: 110=5x. Divide through by 5: 22=x, so x=22.

We should also check that adjacent angles are supplementary: 7y+13+3x-4=180. Let’s check: 118+62=180, so we confirmed that the figure is indeed a parallelogram, and x=22 and y=15 are the solutions.