Question

m∠srt
30deg
m∠str
30deg
m∠rst

Explanation:

Step1: Find \(m\angle STR\)

Since \(\angle STR\) and the \(107^{\circ}\) angle are supplementary (they form a linear pair), we use the formula \(m\angle STR + 107^{\circ}=180^{\circ}\).
So, \(m\angle STR=180^{\circ}- 107^{\circ}=73^{\circ}\).

Step2: Find \(m\angle RST\)

Assuming this is a triangle - related problem (from the figure structure), if we know one angle (\(m\angle STR = 73^{\circ}\)) and assume another given angle (maybe a typo, if we assume the intended value for one of the angles in a triangle - like context, if we consider the sum of angles in a triangle is \(180^{\circ}\)). But if we assume it's a parallelogram - like property (adjacent angles supplementary, but the figure is not clear. However, if we use the exterior - angle - related property (if we consider the triangle \(\triangle RST\) and the linear - pair - derived \(m\angle STR = 73^{\circ}\)). If we assume the problem is about a triangle and one of the given values was mis - written (if we assume the non - \(107^{\circ}\) related angle calculation).
If we use the angle - sum property of a triangle \(\angle SRT+\angle STR+\angle RST = 180^{\circ}\). If \(\angle SRT = 30^{\circ}\) (from the given mis - written input, assuming it's a valid angle for the triangle) and \(\angle STR=73^{\circ}\) (calculated above).
Then \(m\angle RST=180^{\circ}-(30^{\circ}+73^{\circ})=77^{\circ}\).

Answer:

\(m\angle STR = 73^{\circ}\), \(m\angle RST = 77^{\circ}\)