Question

if these two figures are similar, what is the measure of the missing angle?

Explanation:

Step1: Recall triangle angle sum rule

The sum of angles in a triangle is $180^\circ$.

Step2: Confirm similar triangles have congruent angles

Similar figures have identical angle measures.

Step3: Calculate the missing angle

Subtract known angles from $180^\circ$:
$180^\circ - 96^\circ - 42^\circ = 42^\circ$

Answer:

$42^\circ$