Question

In the diagram below of triangle M, N, OMNO, PP is the midpoint of start overline, M, O, end overline
MO
and QQ is the midpoint of start overline, N, O, end overline
NO
. If mangle, O, N, M, equals, 12, plus, 6, x∠ONM=12+6x, and mangle, O, Q, P, equals, minus, 2, x, plus, 60∠OQP=−2x+60, what is the measure of angle, O, Q, P∠OQP?

Answer 1

P and Q are midpoints of MO and NO, so PQ is the midsegment and is parallel to MN. Thus ∠OQP equals ∠ONM, so

12 + 6x = −2x + 60
8x = 48
x = 6.

Then ∠OQP = 12 + 6x = 12 + 36 = 48°.
Answer: 48°.