Question

consider parallelogram abcd.
which equation is made true by the opposite angles theorem?
a. $40 - 2x = 85 + y$
b. $x - 8 = 3y - 15$
c. $3y - 15 = 85 + y$
d. $x - 8 = 40 - 2x$

Explanation:

Step1: Recall opposite angles theorem

In a parallelogram, opposite angles are congruent (equal in measure).

Step2: Identify opposite angles

In parallelogram ABCD, angle A ($(3y-15)^\circ$) and angle C ($(85+y)^\circ$) are opposite angles; angle B and angle D are the other pair of opposite angles.

Step3: Set opposite angles equal

Equate the measures of angle A and angle C:
$3y - 15 = 85 + y$

Answer:

C. $3y - 15 = 85 + y$