Question

question 3 (5 points)
listen
in the figure, if \\( \overline { o q } \\) is the angle bisector of \\( \angle s o t \\), find \\( m \angle q o t \\).
a) \\( 38 ^ { \circ } \\)
b) \\( 46 ^ { \circ } \\)
c) \\( 42 ^ { \circ } \\)
d) \\( 48 ^ { \circ } \\)

Explanation:

Step1: Use the angle - bisector property

Since \( \overrightarrow{OQ}\) is the angle bisector of \( \angle SOT\), then \(m\angle SOQ=m\angle QOT\). So, \(10x + 8=14x-8\).

Step2: Solve the equation for \(x\)

Subtract \(10x\) from both sides: \(8 = 4x-8\).
Add \(8\) to both sides: \(16 = 4x\).
Divide both sides by \(4\): \(x = 4\).

Step3: Find \(m\angle QOT\)

Substitute \(x = 4\) into the expression for \(m\angle QOT\) (\(14x-8\)).
\(m\angle QOT=14\times4 - 8\).
\(m\angle QOT=56 - 8=48^{\circ}\).

Answer:

D. \(48^{\circ}\)