Answer:
m<OPQ = 58°
Explanation:
Question:
In triangle NOP, NP is extended through point P to point Q, m<NOP = (x + 17)°, m<PNO = (2x - 4)°, and m<OPQ = (5x - 17)°. Find m<OPQ.
Solution:
Theorem
In a triangle, the measure of an exterior angle is equal to the sum of the measures of the remote interior angles.
In this triangle, angle OPQ is an exterior angle. Angles NOP and PNO are its remote interior angles.
m<NOP + m<PNO = m<OPQ
x + 17 + 2x - 4 = 5x - 17
3x + 13 = 5x - 17
-2x = -30
x = 15
m<OPQ = 5x - 17 = 5 × 15 - 17 = 58
Answer: m<OPQ = 58°