Question

find the measure of the numbered angle.
35
m∠7 = □°

Explanation:

Step1: Find angle 2

In a right - angled triangle, the sum of angles is \(180^{\circ}\). Given one angle is \(40^{\circ}\) and another is \(90^{\circ}\), then \(\angle2=180^{\circ}-90^{\circ}-40^{\circ}=50^{\circ}\).

Step2: Use vertical - angle property

Since \(\angle1\) and \(\angle2\) are vertical angles, \(\angle1 = \angle2\). So \(\angle1 = 50^{\circ}\).

Step3: Use complementary - angle property

In the right - angled triangle with \(\angle7\), \(\angle1+\angle7 = 90^{\circ}\). Then \(\angle7=90^{\circ}-\angle1\). Substitute \(\angle1 = 50^{\circ}\), we get \(\angle7=90^{\circ}-50^{\circ}=40^{\circ}\).

Answer:

\(40\)