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: Use similarity property

Since the two triangles are similar, their corresponding angles are equal. We can find the missing angle of the first triangle and it will be the same as the missing angle of the second triangle. Let the missing angle of the first triangle be $x$. Then $x + 85^{\circ}+60^{\circ}=180^{\circ}$.

Step3: Solve for the missing angle

$x=180^{\circ}-(85^{\circ} + 60^{\circ})=180^{\circ}-145^{\circ}=35^{\circ}$.

Answer:

$35$