Question

if these two figures are similar, what is the measure of the missing angle? 39° 102° 39° ?

Explanation:

Step1: Recall angle - sum property of a triangle

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

Step2: Calculate the third - angle of the first triangle

Let the missing angle of the first triangle be $x$. Then $x=180-(39 + 102)$.
$x = 180 - 141=39^{\circ}$.

Step3: Use the property of similar triangles

Since the two triangles are similar, corresponding angles are equal. The missing angle in the second triangle corresponds to the $39^{\circ}$ angle in the first triangle.

Answer:

39