Question

1. find the m∠1. 117° 58°

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle to \(117^{\circ}\) and \(117^{\circ}\) form a linear - pair. So, if we let the adjacent interior angle be \(x\), then \(x + 117^{\circ}=180^{\circ}\). Solving for \(x\), we get \(x = 180^{\circ}-117^{\circ}=63^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle1=y\). We know two angles of the triangle: one is \(x = 63^{\circ}\) and the other is \(58^{\circ}\). Then \(y+63^{\circ}+58^{\circ}=180^{\circ}\).

$$y=180^{\circ}-(63^{\circ}+58^{\circ})$$

$$y = 180^{\circ}-121^{\circ}$$

Answer:

\(m\angle1 = 59^{\circ}\)