Question

$\triangle hij \sim \triangle ced$. what is $m\angle d$?
$m\angle d = \square ^\circ$

Explanation:

Step1: Identify congruent angles

Since $\triangle HIJ \sim \triangle CED$, corresponding angles are equal: $\angle H = \angle C = 61^\circ$, $\angle I = \angle E = 30^\circ$, $\angle J = \angle D$.

Step2: Verify angle sum property

The sum of angles in a triangle is $180^\circ$. For $\triangle HIJ$, $\angle H + \angle I + \angle J = 180^\circ$. Substitute known values:
$61^\circ + 30^\circ + \angle J = 180^\circ$

Step3: Solve for $\angle J$ (equal to $\angle D$)

$\angle J = 180^\circ - 61^\circ - 30^\circ = 89^\circ$, so $\angle D = \angle J$.

Answer:

$89$