what is $m\\angle rst$?\nwrite your answer as an integer or decimal.\n$m\\angle rst = \\square ^\\circ$

Explanation:

Step1: Find arc RT measure

First, calculate the measure of arc $RT$. The sum of angles around point $U$ is $360^\circ$. $$m\overset{\frown}{RT} = 360^\circ - 93^\circ - 135^\circ = 132^\circ$$

Step2: Calculate inscribed angle $\angle RST$

$\angle RST$ is an inscribed angle subtended by arc $RT$. The measure of an inscribed angle is half the measure of its subtended arc. $$m\angle RST = \frac{1}{2} \times m\overset{\frown}{RT}$$ $$m\angle RST = \frac{1}{2} \times 132^\circ = 66^\circ$$

Answer:

$66$