Question

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

Explanation:

Step1: Use angle - sum property of a triangle

In the left - hand triangle, the sum of interior angles of a triangle is 180°. Let the angles of the left - hand triangle be 40°, 75°, and ∠1. So, 40°+75° + m∠1=180°.

Step2: Solve for m∠1

m∠1=180°-(40° + 75°)=180° - 115° = 65°.

Step3: Find m∠2

∠2 and the 40° angle are vertical angles. Vertical angles are equal. So, m∠2 = 40°.

Step4: Find m∠3

In the right - hand triangle, one angle is 40° (the given angle) and another is ∠2 = 40°. Using the angle - sum property of a triangle (180° for the sum of interior angles), if the third angle is ∠3, then 40°+40°+m∠3 = 180°. So, m∠3=180°-(40° + 40°)=100°.

Answer:

m∠1 = 65°, m∠2 = 40°, m∠3 = 100°