Question

find the measure of the numbered angle.
34
m∠6=□°

Explanation:

Step1: Find the measure of ∠2

In a right - angled triangle, the sum of angles is \(180^{\circ}\). One angle is \(90^{\circ}\) and another is \(40^{\circ}\). Using the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)), for the triangle with \(40^{\circ}\) and right - angle (\(90^{\circ}\)), \(\angle2=180-(90 + 40)=50^{\circ}\) (vertical angles are equal, and \(\angle2\) and the non - right, non - \(40^{\circ}\) angle in the upper triangle are vertical angles).

Step2: Find the measure of ∠6

\(\angle6\) and \(\angle2\) are alternate exterior angles. By the alternate exterior angles theorem (if two parallel lines are cut by a transversal, then alternate exterior angles are equal). Assuming the two lines with right - angles are parallel (implied by the figure structure), \(m\angle6=m\angle2\)

Answer:

\(50\)