Question

these figures are congruent. what is m∠p?

Explanation:

Step1: Recall congruent - triangle property

Corresponding angles of congruent triangles are equal.

Step2: Identify corresponding angles

In congruent triangles $\triangle JKI$ and $\triangle PQR$, $\angle P$ corresponds to $\angle J$.

Step3: Calculate $\angle J$ in $\triangle JKI$

In right - triangle $\triangle JKI$, we know one angle is $90^{\circ}$ and another is $33^{\circ}$. Using the angle - sum property of a triangle ($\angle J+\angle K+\angle I = 180^{\circ}$, and $\angle K = 90^{\circ}$, $\angle I=33^{\circ}$), so $\angle J=180^{\circ}-90^{\circ}-33^{\circ}=57^{\circ}$.

Step4: Find $\angle P$

Since $\angle P=\angle J$ (corresponding angles of congruent triangles), $m\angle P = 57^{\circ}$.

Answer:

$57$