Question

find the measure of the numbered angle.
29
m∠1=□°

Explanation:

Step1: Find the third angle of the right - angled triangle

In a right - angled triangle, the sum of angles is \(180^{\circ}\). One angle is \(90^{\circ}\) and another is \(40^{\circ}\). Let the third angle be \(x\). Then \(x+90^{\circ}+40^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(90^{\circ}+40^{\circ})=50^{\circ}\).

Step2: Use the property of vertical angles

\(\angle1\) and the angle \(x\) (calculated as \(50^{\circ}\)) are vertical angles. Vertical angles are equal.

Answer:

\(50\)