Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A line segment ACD is shown with triangle ABC drawn so that AC is the base of the triangle. Angle BAC is labeled with 72 degree sign, and angle BCD is labeled with 113 degree sign. Write a list of steps that are needed to find the measure of ∠ B . Please help soon!!

Answer 1

41°

Explanation:

Given ∆ABC with exterior angle DCB as 113° and remote interior angle A as 72°, you want the measure of angle B.

Exterior angle theorem

The exterior angle theorem tells you that an exterior angle of a triangle is the sum of the two remote interior angles.

This means we can find the value of one of the remote interior angles by subtracting the other one from the exterior angle.

Step 1: subtract angle A from exterior angle BCD to find angle B.

∠B = 113° -72° = 41°

The measure of angle B is 41°.

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Additional comment

The first step is to be familiar with the angle relations around a triangle. As you can see, making use of the appropriate relation to find the desired angle is a trivial matter.