Question

find the measure of the unknown angle (marked with ?), given angles of 30° and 20° in the diagram.

Explanation:

Step1: Identify alternate interior angles

The 30° angle and the angle adjacent to the unknown angle (along the transversal) are alternate interior angles, so they are equal.

Step2: Use triangle exterior angle property

The unknown angle is equal to the sum of the 30° angle and the 20° angle (exterior angle of a triangle equals sum of two non-adjacent interior angles).
<Expression>
$? = 30^\circ + 20^\circ = 50^\circ$
</Expression>

Answer:

$50^\circ$