Question

in exercises 13 and 14, find ( mangle 1 ). (see example 4.)
13.
14.

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle LMN\) and \(\triangle XYZ\), since they are congruent (by the given right - angle markings and the way the triangles are presented, we assume they are congruent), the corresponding angles are equal. In \(\triangle LMN\), we know one right angle (\(90^{\circ}\)) and \(\angle L = 70^{\circ}\).

Step2: Calculate \(\angle1\)

Using the formula \(m\angle1+90^{\circ}+70^{\circ}=180^{\circ}\). Then \(m\angle1=180^{\circ}-(90^{\circ} + 70^{\circ})\).

$$m\angle1=180^{\circ}-160^{\circ}=20^{\circ}$$

Answer:

\(20^{\circ}\)