Question

determining central and inscribed angles in circles

step - by - step example
how can you calculate the value of ( mangle mxq ) given the value of ( mwidehat{mq} )?
since ( angle mxq ) is an inscribed angle in the circle, ( mangle mxq=\frac{1}{2}mwidehat{mq} ).
the ( mangle mxq ) is
reason:

Explanation:

Step1: Recall inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. So, $m\angle MXQ = \frac{1}{2}m\widehat{MQ}$.

Step2: Substitute the given arc measure

Given $m\widehat{MQ} = 121.7^\circ$, calculate $m\angle MXQ = \frac{1}{2} \times 121.7^\circ$.

Answer:

60.85°