Question

In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle PNO = (x+14)^{\circ}m∠PNO=(x+14) ∘ , \text{m}\angle OPQ = (5x-2)^{\circ}m∠OPQ=(5x−2) ∘ , and \text{m}\angle NOP = (x-1)^{\circ}m∠NOP=(x−1) ∘ . Find \text{m}\angle OPQ.M∠OPQ.

Answer 1

Answer:

<OPQ = 23 degrees

Step-by-step explanation:

Given

Interior angles m∠PNO=(x+14) and m∠NOP=(x−1)

Exterior angle = m<OPQ = (5x-2)

The sum of interior angles is equal to the exterior angle, that is;

m∠PNO+m∠NOP = m<OPQ

x+14 + x-1 = 5x-2

2x + 13 = 5x-2

Collect like terms;

2x-5x = -2-13

-3x = -15

x = 15/3

x = 5

Get <OPQ

<OPQ = 5x - 2

<OPQ = 5(5)- 2

<OPQ = 25-2

<OPQ = 23 degrees