Question

In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle OPQ = (9x-19)^{\circ}m∠OPQ=(9x−19) ∘ , \text{m}\angle PNO = (2x+5)^{\circ}m∠PNO=(2x+5) ∘ , and \text{m}\angle NOP = (3x+16)^{\circ}m∠NOP=(3x+16) ∘ . Find \text{m}\angle NOP.M∠NOP.

Answer 1

Answer:

To find the measure of angle OPQ, we have two equations...

y+5x-17=180 because angles OPN and OPQ are supplementary...

AND

x+17+2x-4+y=180 because the total degrees of a triangle must add up to 180.

The equations...

5x+y=197

3x+y=167

solce the system of equations...

x=15

y=122

Since we wanted to solve for y, 122 is the answer.

The measure of angle OPQ is 122.