Question

1. 2) find the measure of each angle indicated. 11. find the missing angle measure.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Also, an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Solve for the angle in problem 10

In triangle ABC, ∠ACM is an exterior angle. Let the unknown angle ∠ABC be x. We know that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, ∠ACM=∠A + ∠B. Given ∠A = 70° and ∠ACM = 110°. Then 110°=70°+x. Solving for x: x=110° - 70° = 40°.

Step3: Solve for the angle in problem 11

Let the unknown angle be b. Using the angle - sum property of a triangle, if the other two angles of the triangle are 119° and 34°, then b+119°+34° = 180°. First, add the known angles: 119°+34°=153°. Then, solve for b: b = 180°-153°=27°.

Answer:

For problem 10, the measure of the indicated angle is 40°.
For problem 11, the measure of the indicated angle is 27°.