Question

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

Explanation:

Step1: Match congruent triangle angles

Congruent triangles have identical corresponding angles. $\angle H = 42^\circ$ corresponds to $\angle N = 42^\circ$.

Step2: Identify corresponding angle for $\angle I$

$\angle I$ corresponds to $\angle O$, which is $78^\circ$.
(Alternatively, calculate $\angle I$ using triangle angle sum:
Sum of angles in triangle = $180^\circ$.
$\angle I = 180^\circ - 42^\circ - m\angle G$. Since $\angle G$ corresponds to $\angle P = 60^\circ$, $\angle I = 180^\circ - 42^\circ - 60^\circ = 78^\circ$)

Answer:

$78$