Question

1. if a ray qt bisects ∠rqs, what is m∠tqs?

Explanation:

Step1: Recall bisector definition

A ray that bisects an angle divides the angle into two equal - measure angles.
If ray \(QT\) bisects \(\angle RQS\), then \(\angle RQT=\angle TQS\) and \(m\angle RQS = m\angle RQT + m\angle TQS\).

Step2: Express relationship

Since \(\angle RQT=\angle TQS\), we can say \(m\angle RQS = 2m\angle TQS\), so \(m\angle TQS=\frac{m\angle RQS}{2}\)

Answer:

We need the measure of \(\angle RQS\) to find \(m\angle TQS\). If \(m\angle RQS = x\), then \(m\angle TQS=\frac{x}{2}\)