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 intersecting outside a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs are $\stackrel{\frown}{MR}$ (97°) and $\stackrel{\frown}{PS}$ (19°).

Step3: Calculate the angle

$m\angle PQS = \frac{1}{2}(m\stackrel{\frown}{MR} - m\stackrel{\frown}{PS})$
$m\angle PQS = \frac{1}{2}(97^\circ - 19^\circ)$
$m\angle PQS = \frac{1}{2}(78^\circ)$

Answer:

$39^\circ$