Question

7 if ( mangle1 = 53^{circ} ), what is ( mangle3 )?

Explanation:

Step1: Find the measure of angle 2

In right - triangle \(DEF\) (\(\angle D = 90^{\circ}\)), using the angle - sum property of a triangle (\(\angle1+\angle2 + \angle D=180^{\circ}\)).
Substitute \(\angle1 = 53^{\circ}\) and \(\angle D = 90^{\circ}\) into the formula:
\(53^{\circ}+\angle2+90^{\circ}=180^{\circ}\)
\(\angle2=180^{\circ}-(90^{\circ} + 53^{\circ})\)
\(\angle2 = 37^{\circ}\)

Step2: Find the measure of angle 3

Since \(\angle2\) and \(\angle3\) are supplementary (\(\angle2+\angle3 = 180^{\circ}\), linear - pair of angles).
Substitute \(\angle2 = 37^{\circ}\) into the formula:
\(\angle3=180^{\circ}-\angle2\)
\(\angle3=180^{\circ}- 37^{\circ}\)
\(\angle3 = 143^{\circ}\)

Answer:

\(143^{\circ}\)