Question

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

Explanation:

Step1: Use the property of vertical angles and linear pairs

Since \(\angle TRV\cong\angle VRW\), and \(\angle TRV + \angle VRW= 180^{\circ}\) (linear pair of angles). Let \(m\angle TRV = m\angle VRW=x\). Then \(x + x=180^{\circ}\), so \(2x = 180^{\circ}\), and \(x = 90^{\circ}\). Also, \(\angle SRT\) and \(\angle VRW\) are vertical angles.

Step2: Apply the vertical - angle theorem

By the vertical - angle theorem, if two angles are vertical angles, then they are congruent. So \(m\angle SRT=m\angle VRW\)

Answer:

\(90\)