Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

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

Step2: Set up the equation

Let the third - angle of the triangle be \(x\). We know two angles are 59° and 57°. So, \(x + 59^{\circ}+57^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x=180^{\circ}-(59^{\circ} + 57^{\circ})=180^{\circ}-116^{\circ}=64^{\circ}\).

Step4: Find \(m\angle1\)

\(\angle1\) and the third - angle of the triangle are supplementary (a straight - line is 180°). So, \(m\angle1 = 180^{\circ}-64^{\circ}=116^{\circ}\).

Answer:

\(116^{\circ}\)