Question

what are the measures of \\( \angle 1 \\) and \\( \angle 2 \\)? explain.
the measure of \\( \angle 1 \\) is \\( \square \\) because it is related to one of the angles of the triangle by the
(type an integer or a decimal. do not include the degree symbol in your answer.)

Explanation:

Step1: Identify the triangle type

The triangle has two equal - length sides (marked with the same tick marks), so it is an equilateral triangle. In an equilateral triangle, each interior angle is \(60^{\circ}\).

Step2: Use the property of parallel lines and alternate interior angles

Since the lines are parallel, \(\angle1\) is equal to the interior angle of the equilateral triangle. So \(\angle1 = 60\) (by the alternate - interior angles theorem).

Step3: Use the property of exterior angles of a triangle

For \(\angle2\), in the equilateral triangle, using the exterior - angle theorem. The exterior angle \(\angle2\) is equal to the sum of the two non - adjacent interior angles. Each interior angle of the equilateral triangle is \(60^{\circ}\), so \(\angle2=60 + 60=120\) (by the exterior - angle theorem).

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), and the measure of \(\angle2\) is \(120\) (because it is related to the angles of the triangle by the exterior - angle theorem).