Question

what is $m\angle q$?
write your answer as an integer or decimal.
$m\angle q = \square^\circ$
$63^\circ$

Explanation:

Step1: Identify inscribed angle property

The inscribed angle $\angle R = 63^\circ$ subtends arc $ST$.

Step2: Calculate arc $ST$ measure

The measure of arc $ST$ is twice the inscribed angle:
$m\overset{\frown}{ST} = 2 \times 63^\circ = 126^\circ$

Step3: Find total circle angle

A full circle is $360^\circ$. Calculate the remaining arc:
$m\overset{\frown}{SRT} = 360^\circ - 126^\circ = 234^\circ$

Step4: Relate central angle to arc

The central angle $\angle Q$ subtends arc $SRT$, so $m\angle Q = m\overset{\frown}{SRT} = 234^\circ$

Answer:

237