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°. Let the third - interior angle of the triangle be \(x\). Then \(x + 62^{\circ}+57^{\circ}=180^{\circ}\).

Step2: Calculate the third - interior angle

\[

$$\begin{align*} x&=180^{\circ}-(62^{\circ} + 57^{\circ})\\ x&=180^{\circ}-119^{\circ}\\ x& = 61^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

\(\angle1\) and the third - interior angle of the triangle form a linear pair. A linear pair of angles sums to 180°. So \(m\angle1=180^{\circ}-61^{\circ}\).

Step4: Calculate \(m\angle1\)

\(m\angle1 = 119^{\circ}\)

Answer:

\(119\)