Question

find $m\angle 1$.
(there is a diagram with two right triangles, triangle lmn with a right angle at n and angle at l of 70 degrees, and triangle xyz with a right angle at y, and angle 1 at x. the question is to find the measure of angle 1, with a box to fill in the degree measure.)
$m\angle 1 = \square ^\circ$

Explanation:

Step1: Recall triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\).

Step2: Calculate \(m\angle1\)

In \(\triangle LNM\), \(\angle L = 70^{\circ}\), \(\angle N=90^{\circ}\). In \(\triangle XYZ\), \(\angle Y = 90^{\circ}\).
Since the two triangles are similar (by AA similarity, as two right - angles and other angles are equal in proportion), \(m\angle1\) can be found using \(180^{\circ}-90^{\circ}-70^{\circ}\).

$$180^{\circ}-90^{\circ}-70^{\circ}=20^{\circ}$$

Answer:

\(20\)