Question

rstuv ~ fghij. what are ( mangle s ) and ( mangle f )?
( mangle s = square^circ )
( mangle f = 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 $m\angle S$

Sum known angles in RSTUV: $111^\circ+100^\circ+129^\circ+111^\circ = 451^\circ$. Subtract from total:
$$m\angle S = 540^\circ - 451^\circ = 131^\circ$$

Step3: Match congruent angles (similar polygons)

Similar polygons have congruent corresponding angles. $\angle F$ corresponds to $\angle U$, so:
$$m\angle F = m\angle U = 129^\circ$$

Answer:

$m\angle S = 131^\circ$, $m\angle F = 129^\circ$