Question

In triangle NOP, NP is extended through point P to point Q, m∠PNO = (x + 14)°, m∠OPQ = (5x – 2), and m∠NOP = (x - 1)º. Find m∠OPQ.

Answer 1

23 degrees

Step-by-step explanation:

The diagram representing this question is drawn and attached below:

Theorem: The exterior angle of a triangle is equal to the sum of the opposite interior angles.

Applying the theorem above gives:

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

We solve for x.

`\begin{gathered} 2x+13=5x-2 \\ 5x-2x=13+2 \\ 3x=15 \\ x=(15)/(3) \\ x=5 \end{gathered}`

Therefore, the measure of angle OPQ will be:

`\begin{gathered} m\angle\text{OPQ}=5x-2 \\ =5(5)-2 \\ =25-2 \\ =23\degree \end{gathered}`