Question

In ΔNOP, \overline{NP} NP is extended through point P to point Q, m∠OPQ = (6x-15)∘, m∠PNO=(2x+18)∘ , and m∠NOP=(2x−13)∘. What is the value of x?

Answer 1

By utilizing the properties of triangle angle sums and exterior angles, it is determined that the value of x is 10.

Step-by-step explanation:

To find the value of x in ∆NOP, we can use the fact that the sum of the interior angles of a triangle is equal to 180 degrees.

Given that:

Thus, we have:

(6x - 15)° = (2x + 18)° + (2x − 13)°

Combining like terms and solving for x, we get:

6x - 15 = 2x + 18 + 2x - 13

6x - 15 = 4x + 5

6x - 4x = 5 + 15

2x = 20

x = 10