Question

what are the measures of ∠1 and ∠2? explain.
the measure of ∠1 is 60 because it is related to one of the angles of the triangle by the alternate interior angles theorem.
(type an integer or a decimal. do not include the degree symbol in your answer.)
the measure of ∠2 is 60 because it is one of the angles in the triangle.
(type an integer or a decimal. do not incl er.)

Explanation:

Since the triangle has equal - length sides (marked with the same tick marks), it is an equilateral triangle. In an equilateral triangle, each interior angle is \(60^{\circ}\). For \(\angle1\), by the Alternate Interior Angles Theorem (if two parallel lines are cut by a transversal, alternate interior angles are equal), it is equal to one of the interior angles of the equilateral triangle. For \(\angle2\), by the Corresponding Angles Theorem (if two parallel lines are cut by a transversal, corresponding angles are equal), it is equal to one of the interior angles of the equilateral triangle.

Answer:

The measure of \(\angle1\) is \(60\) because it is related to one of the angles of the triangle by the Alternate Interior Angles Theorem. The measure of \(\angle2\) is \(60\) because it is a corresponding angle to one of the angles in the triangle.