Let's find the value of each variable one at a time.
Value of x
The angles that measure 12x + 72 and 25x + 20 are opposite angles. Recall the Theorem 6.10, which tells us that if both pairs of opposite angles in quadrilateral are congruent, then the quadrilateral is a parallelogram. Therefore, the measures of these angles must be equal.
12x + 72= 25x + 20
Let's solve this equation to find a value of x.
Similarly, the angles that measure 9y - 12 and 3y + 36 are also opposite angles. Recall the same theorem once again. The measures of these angles must be equal.
9y - 12= 3y + 36
Let's solve the equation to find a value of y.
