Question

uvwxy ~ tpqrs. what is ( mangle s )?( mangle s = square^circ )

Explanation:

Step1: Find sum of pentagon angles

The formula for the sum of interior angles of an n-sided polygon is $(n-2)\times180^\circ$. For a pentagon ($n=5$):
$$(5-2)\times180^\circ = 540^\circ$$

Step2: Calculate $\angle V$ in UVWXY

Subtract known angles from total sum:
$$m\angle V = 540^\circ - 90^\circ - 137^\circ - 98^\circ - 97^\circ = 118^\circ$$

Step3: Match corresponding angles

Similar polygons have congruent corresponding angles. $\angle S$ corresponds to $\angle V$, so $m\angle S = m\angle V$.

Answer:

$118$