Question

now its time to practice on your own
here is circle o.
what is $m\angle pqs$?
enter your answer in the box.
$\square^\circ$

Explanation:

Step1: Recall exterior angle theorem

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs. The intercepted arcs are $\overset{\frown}{MR}$ (83°) and $\overset{\frown}{PS}$ (21°).

Step2: Calculate the angle

Use the formula: $m\angle PQS = \frac{1}{2}(m\overset{\frown}{MR} - m\overset{\frown}{PS})$
Substitute values: $\frac{1}{2}(83^\circ - 21^\circ) = \frac{1}{2}(62^\circ)$

Answer:

$31^\circ$