Question

these figures are congruent. what is ( mangle q )?

Explanation:

Step1: Match congruent polygon sides

Identify corresponding sides: $HG = PO = 33\ \text{cm}$, $JI = QN = 13\ \text{cm}$, $HI = ON = 48\ \text{cm}$. So the congruence is $GHIJ \cong PONQ$, meaning $\angle Q$ corresponds to $\angle J$.

Step2: Verify sum of quadrilateral angles

Sum of interior angles of a quadrilateral is $(4-2)\times180^\circ = 360^\circ$. For $GHIJ$, confirm: $m\angle G + 122^\circ + 85^\circ + m\angle H = 360^\circ$. For $PONQ$: $50^\circ + 103^\circ + m\angle N + m\angle Q = 360^\circ$. Since congruent angles match, $\angle Q = \angle J$.

Answer:

$122$