Question

m∠srt
32deg
m∠str
65deg
m∠rst

Explanation:

Step1: Find \(m\angle STR\)

Since \(\angle STR\) and the \(115^{\circ}\) angle are supplementary (they form a linear pair), we use the formula \(m\angle STR = 180^{\circ}-115^{\circ}\).
\(m\angle STR=65^{\circ}\)

Step2: Find \(m\angle SRT\)

Since \(\angle SRT\) and the \(148^{\circ}\) angle are supplementary (they form a linear pair), we use the formula \(m\angle SRT = 180^{\circ}-148^{\circ}\).
\(m\angle SRT = 32^{\circ}\)

Step3: Find \(m\angle RST\)

Use the triangle - angle sum theorem (\(m\angle RST+m\angle SRT+m\angle STR=180^{\circ}\)). Substitute \(m\angle SRT = 32^{\circ}\) and \(m\angle STR=65^{\circ}\) into the formula:
\(m\angle RST=180^{\circ}-(32^{\circ}+65^{\circ})\)
\(m\angle RST=180^{\circ}-97^{\circ}\)
\(m\angle RST = 83^{\circ}\)

Answer:

\(m\angle RST = 83^{\circ}\)