Question

in the figure below, ray ( overrightarrow{qs} ) bisects ( angle rqt ), and ( angle rqt = 60^{circ} ). what is the value of ( x )?

Explanation:

Step1: Recall the angle - bisector definition

Since ray \(\overrightarrow{QS}\) bisects \(\angle RQT\), then \(\angle RQS=\frac{1}{2}\angle RQT\).
Given \(\angle RQT = 60^{\circ}\), so \(\angle RQS=\frac{1}{2}\times60^{\circ}=30^{\circ}\).

Step2: Solve for \(x\)

We know that \(\angle RQS = 3x^{\circ}\).
Set up the equation \(3x=30\).
Divide both sides of the equation by \(3\): \(x=\frac{30}{3}\).

Answer:

\(x = 10\), so the answer is B.