Question

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

Explanation:

Step1: Recall angle - sum property of triangles

The sum of interior angles of a triangle is 180°.

Step2: Calculate the missing angle

Let the missing angle be $x$. We know two angles of the first triangle are 42° and 96°. For the second similar triangle, we use the angle - sum property. So, $x=180-(42 + 96)$.
$x = 180 - 138$
$x=42$

Answer:

42