Question

question 29 (5 points)
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if \\( \overrightarrow { q s } \\) is an angle bisector of \\( \angle p q r \\) and \\( m \angle p q r = 140 ^ { \circ } \\), find the measure of \\( \angle p q s \\).
\\( 100 ^ { \circ } \\)
\\( 280 ^ { \circ } \\)
\\( 140 ^ { \circ } \\)
\\( 70 ^ { \circ } \\)

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector divides an angle into two equal parts. So, if \( \overrightarrow{QS}\) bisects \( \angle PQR\), then \( m\angle PQS=\frac{1}{2}m\angle PQR\).

Step2: Substitute the given value of \( m\angle PQR\)

Given \( m\angle PQR = 140^{\circ}\). Substitute into the formula: \( m\angle PQS=\frac{1}{2}\times140^{\circ}\).

$$m\angle PQS = 70^{\circ}$$

Answer:

\(70^{\circ}\) (the fourth option)