: 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
.
To find the measure of angle B, we can use the fact that the sum of the angles in a triangle is 180 degrees. Here are the steps:
1. Draw a diagram of the line segment ACD and triangle ABC as described in the problem.
2. Label angle B as x degrees.
3. Use the fact that angle BAC is 72 degrees to find the measure of angle A:
angle A = 180 - angle BAC - angle BCD
= 180 - 72 - 113
= 5 degrees
4. Use the fact that AC is the base of the triangle to find the measure of angle C:
angle C = 180 - angle A - angle B
= 180 - 5 - x
= 175 - x degrees
5. Use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle B:
angle A + angle B + angle C = 180
5 + x + (175 - x) = 180
180 = 180
6. Solve for x:
5 + x + 175 - x = 180
180 - 180 = -5 + x - x
-5 = -2x
x = 2.5
7. Check your answer:
angle A + angle B + angle C = 180
5 + 2.5 + (175 - 2.5) = 180
180 = 180
Therefore, the measure of angle B is 2.5 degrees.