Question

9 find m\angle 1.
53°
87°
66°
73°

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle to \(124^{\circ}\) is \(180^{\circ}- 124^{\circ}=56^{\circ}\) (supplementary angles).

Step2: Use the triangle - angle sum theorem

In a triangle, the sum of interior angles is \(180^{\circ}\). Let the angle we found in Step1 be \(x = 56^{\circ}\), the given angle be \(y=37^{\circ}\), and \(\angle1\) be \(z\). Then \(x + y+z=180^{\circ}\).
Substitute \(x = 56^{\circ}\) and \(y = 37^{\circ}\) into the equation: \(z=180^{\circ}-(56^{\circ}+37^{\circ})\).
Calculate \(56^{\circ}+37^{\circ}=93^{\circ}\).
Then \(z = 180^{\circ}-93^{\circ}=87^{\circ}\).

Answer:

\(87^{\circ}\)