Question

find the measure of the numbered angle.

m∠5 = □°

Explanation:

Step1: Find the measure of ∠1

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

$$m\angle1=180^{\circ}-(90^{\circ} + 40^{\circ})=50^{\circ}$$

Step2: Use vertical - angle property

Since ∠1 and ∠3 are vertical angles, \(m\angle3 = m\angle1 = 50^{\circ}\)

Step3: Use the right - angle and angle - sum property

In the lower right - angled part, one angle is \(90^{\circ}\). Let's consider the triangle where ∠3 and ∠5 are angles.

$$m\angle5=180^{\circ}-(90^{\circ}+m\angle3)$$

Substitute \(m\angle3 = 50^{\circ}\)

$$m\angle5=180^{\circ}-(90^{\circ}+50^{\circ}) = 40^{\circ}$$

Answer:

\(40\)