Question

find the measures of angles 1, 2, and 3. (hint: find m∠1, then m∠2, and then m∠3.) the measure of angle 1 is 65°. (simplify your answer. type an integer or a decimal.) the measure of angle 2 is (simplify your answer. type an integer or a decimal.) (the figure is not to scale.)

Explanation:

Step1: Find measure of angle 1

Use the angle - sum property of a triangle. In the small triangle with angle 1, the other two angles are 75° and 40°. The sum of the interior angles of a triangle is 180°. So, \(m\angle1=180-(75 + 40)=180 - 115=65^{\circ}\).

Step2: Find measure of angle 2

In the large triangle, one angle is 35° and the angle adjacent to angle 1 (in the large - triangle context) is also 65°. Using the angle - sum property of a triangle again, \(m\angle2=180-(65 + 35)=180 - 100 = 80^{\circ}\).

Step3: Find measure of angle 3

We know that the sum of angles in the large triangle is 180°. We already found the other two non - angle 3 angles. So \(m\angle3=180-(75+35)=70^{\circ}\)

Answer:

\(m\angle1 = 65^{\circ}\), \(m\angle2 = 80^{\circ}\), \(m\angle3 = 70^{\circ}\)