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 40°. (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Calculate m∠3

We know m∠1 = 65° and m∠2 = 40°. Let m∠3 be the third - angle of the triangle. Then, by the angle - sum property of a triangle, m∠1+m∠2 + m∠3=180°. So, m∠3=180°-(m∠1 + m∠2). Substitute m∠1 = 65° and m∠2 = 40° into the formula: m∠3=180°-(65° + 40°)=180° - 105° = 75°.

Answer:

m∠1 = 65°, m∠2 = 40°, m∠3 = 75°