Question

in the diagram, \\( \angle trv \cong \angle vrw \\) what is the measure of \\( \angle srt? \\) \\( m\angle srt= \\) degrees

Explanation:

Step1: Find the measure of \(\angle TRV\) and \(\angle VRW\)

Since \(\angle TRV+\angle VRW = 120^{\circ}\) (linear - pair adjacent angles) and \(\angle TRV\cong\angle VRW\), then \(\angle TRV=\angle VRW=\frac{120^{\circ}}{2} = 60^{\circ}\)

Step2: Use the property of vertical angles

\(\angle SRT\) and \(\angle VRW\) are vertical angles. By the vertical - angles theorem (vertical angles are congruent), \(m\angle SRT=m\angle VRW\)
So \(m\angle SRT = 60^{\circ}\)

Answer:

\(60\)