Question

for the figure shown, find m∠1. (the figure is not drawn to scale.) m∠1 = □°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Let the third - interior angle of the triangle be \(x\).

We know two interior angles of the triangle are 57° and 63°. So, \(x+57 + 63=180\). Then \(x = 180-(57 + 63)=180 - 120 = 60^{\circ}\).

Step3: Use the linear - pair property

\(\angle1\) and the third - interior angle \(x\) form a linear pair. A linear pair of angles add up to 180°. So, \(m\angle1=180 - x\).
Since \(x = 60^{\circ}\), then \(m\angle1=120^{\circ}\).

Answer:

120