Question

if these two figures are similar, what is the measure of the missing angle? 30° 120° 30° ?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is $180^{\circ}$.

Step2: Recall property of similar triangles

Similar triangles have equal corresponding angles.

Step3: Calculate the missing angle

Let the missing angle be $x$. For the first triangle, with angles $30^{\circ}$, $120^{\circ}$, and $30^{\circ}$, we know that for the similar triangle, the missing angle $x$ corresponds to one of the angles of the first triangle. Since the sum of angles in a triangle is $180^{\circ}$, and the two given angles in the first triangle are $30^{\circ}$ and $120^{\circ}$, we can also calculate the third - angle of the first triangle as $180-(30 + 120)=30^{\circ}$. The missing angle in the second (similar) triangle is also $30^{\circ}$ because corresponding angles of similar triangles are equal.

Answer:

$30^{\circ}$