Question

In ANOP, NP is extended through point P to point Q,

mZOPQ = (6x – 15)°, mZPNO = (2x + 18)°, and
mZNOP = (2x – 13). What is the value of x?

Answer 1

x = 10

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