Answer:
x = 10
Step-by-step explanation:
Form the information given, we can deduce that:
m<OPQ is an exterior angle of ∆NOP = (6x - 15)°
m<PNO = (2x + 18)° and m<NOP = (2x - 13)° are both interior angles that are opposite to the exterior angle.
Therefore, based on the exterior angle theorem:
m<OPQ = m<PNO + m<NOP
(6x - 15)° = (2x + 18)° + (2x - 13)°
Solve for x
6x - 15 = 2x + 18 + 2x - 13
6x - 15 = 4x + 5
6x - 15 - 4x = 4x + 5 - 4x (Subtraction property of equality)
2x - 15 = 5
2x - 15 + 15 = 5 + 15 (addition property of equality)
2x = 20
2x/2 = 20/2 (division property of equality)
x = 10
