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In triangle NOP, line NP is extended through point P to Q, m

User Mttmllns
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1 Answer

15 votes
15 votes

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°

User Treziac
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