Question

in the diagram, ∠trv ≅ ∠vrw. what is the measure of ∠srt? m∠srt = degrees

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. Since \(\angle TRV\cong\angle VRW\), and \(\angle TRV\) and \(\angle SRW\) are vertical angles (so \(\angle TRV = \angle SRW\)), also \(\angle TRV=\angle VRW\).

Step2: Use the fact that a straight - line angle is \(180^{\circ}\)

Let \(m\angle TRV = m\angle VRW=x\). The sum of angles around a straight line: \(\angle TRV+\angle VRW+\angle SRT = 180^{\circ}\). But since \(\angle TRV=\angle VRW\), and we know that \(\angle TRV + \angle VRW+\angle SRT=180^{\circ}\), and \(\angle TRV=\angle VRW = 60^{\circ}\) (assuming from the standard problem setup where these angles are equal and form a linear - pair with \(\angle SRT\) such that \(x + x+\angle SRT=180^{\circ}\), if \(x = 60^{\circ}\)).

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If \(x = 60^{\circ}\), then \(\angle SRT=180^{\circ}-120^{\circ}\)

Answer:

\(60\)