Question

question 7 of 10
if pqrs is a rectangle and m∠rsq = 36°, what is the value of x?
a. 54
b. 108
c. 94
d. 72
e. 36
f. cannot be determined

Explanation:

Step1: Alternate interior angles

∠RSQ = ∠PQS = 36° (SR||PQ, SQ transversal)

Step2: Isosceles triangle OQP

OQ = OP (diagonals bisect/equal), so ∠OPQ = ∠OQP = 36°

Step3: Sum of angles in △OQP

∠POQ = 180° - 36° - 36° = 108° (x = ∠POQ)

Answer:

B. 108