Question

$\triangle pqr \sim \triangle hji$. what are $m\angle i$ and $m\angle p$?
$m\angle i = \square^\circ$
$m\angle p = \square^\circ$

Explanation:

Step1: Find $\angle P$ in $\triangle PQR$

The sum of angles in a triangle is $180^\circ$.
$\angle P = 180^\circ - 36^\circ - 89^\circ = 55^\circ$

Step2: Use similarity for $\angle I$

Similar triangles have congruent corresponding angles. $\angle I$ corresponds to $\angle R$, so $m\angle I = 89^\circ$.

Step3: Match $\angle P$ to corresponding angle

$\angle P$ corresponds to $\angle H$, so $m\angle P = 55^\circ$.

Answer:

$m\angle I = 89^\circ$, $m\angle P = 55^\circ$