Question

question 9 (5 points)
listen
in the figure, if \\( \overrightarrow { o q } \\) is the angle bisector of \\( \angle p o r \\), find \\( m \angle p o q \\).
a) \\( 31 ^ { \circ } \\)
b) \\( 6 ^ { \circ } \\)
c) \\( 61 ^ { \circ } \\)
d) \\( 30.5 ^ { \circ } \\)

Explanation:

Step1: Use the angle - bisector property

Since \( \overrightarrow{OQ}\) is the angle bisector of \( \angle POR\), then \(m\angle POQ=m\angle QOR\). So, \(9x + 7=13x-17\).

Step2: Solve the equation for \(x\)

Subtract \(9x\) from both sides: \(7 = 4x-17\).
Add \(17\) to both sides: \(4x=7 + 17=24\).
Divide both sides by \(4\): \(x = 6\).

Step3: Find \(m\angle POQ\)

Substitute \(x = 6\) into \(9x+7\). Then \(m\angle POQ=9x+7=9\times6 + 7\).
Calculate \(9\times6+7=54 + 7=61\).

Answer:

C. \(61^{\circ}\)