Question

john lays tile for a living. while trying to create the perfect design for his client, he drew this pattern containing two right triangles and an isosceles triangle. for the triangles to fit together perfectly, john must determine the measure of angles 1, 2, and 3. what is the measure of angle 1? what is the measure of angle 2? what is the measure of angle 3?

Explanation:

Step1: Find angle 1

In a right - triangle, the sum of the two non - right angles is \(90^{\circ}\).
Since one of the non - right angles is \(32^{\circ}\), then \(\angle1 = 90^{\circ}-32^{\circ}=58^{\circ}\)

Step2: Find angle 2

The sum of angles around a point on a straight line is \(180^{\circ}\).
We know the two \(32^{\circ}\) angles and \(\angle2\) form a straight line. So \(\angle2=180^{\circ}-32^{\circ}-32^{\circ}=116^{\circ}\)

Step3: Find angle 3

In the right - triangle on the right, the sum of the two non - right angles is \(90^{\circ}\).
Since one of the non - right angles is \(32^{\circ}\), then \(\angle3 = 90^{\circ}-32^{\circ}=58^{\circ}\)

Answer:

Angle 1: \(58\)
Angle 2: \(116\)
Angle 3: \(58\)