Question

find the measure of the numbered angle.
m∠7 = □°

Explanation:

Step1: Find the measure of ∠1

In a right - angled triangle, the sum of angles is \(180^{\circ}\). Given one angle is \(40^{\circ}\) and another is \(90^{\circ}\).
\(\angle1=180^{\circ}-(40^{\circ} + 90^{\circ})=50^{\circ}\)

Step2: Use vertical - angle property

\(\angle3=\angle1\) (vertical angles are equal). So \(\angle3 = 50^{\circ}\)

Step3: Find the measure of ∠7

In a right - angled situation (the right angle and \(\angle3\) and \(\angle7\) are related as the sum of angles in a triangle - like part). \(\angle7=180^{\circ}-(90^{\circ}+\angle3)\)
Substitute \(\angle3 = 50^{\circ}\)
\(\angle7=180^{\circ}-(90^{\circ}+50^{\circ}) = 40^{\circ}\)

Step4: Use vertical - angle property for ∠7 and ∠8

\(\angle8=\angle7\) (vertical angles are equal)

Answer:

\(40\)