Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

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

Step2: Calculate the missing angle

Let the missing angle be $x$. We have $x + 39^{\circ}+39^{\circ}=180^{\circ}$. Then $x=180^{\circ}-(39^{\circ}+39^{\circ})$. First, $39^{\circ}+39^{\circ}=78^{\circ}$. Then $x = 180^{\circ}-78^{\circ}=102^{\circ}$. Also, for similar triangles, corresponding angles are equal. The first triangle has angles 102°, 39°, 39° and the missing angle corresponds to the 102° angle in the similar - triangle.

Answer:

$102$