Question

these figures are congruent. what is $m\angle g$?

Explanation:

Step1: Sum of quadrilateral angles

The sum of interior angles of a quadrilateral is $360^\circ$.

Step2: Identify congruent angle pairs

Since the figures are congruent:
$\angle F = \angle R = 92^\circ$, $\angle H = \angle O = 72^\circ$, $\angle I = \angle Q = 50^\circ$, and $\angle G = \angle P$.

Step3: Calculate $\angle G$

Subtract known angles from $360^\circ$:
$\angle G = 360^\circ - 92^\circ - 72^\circ - 50^\circ$
$\angle G = 360^\circ - 214^\circ = 146^\circ$

Answer:

$146$