Question

One angle of a triangle has a measure of 36°. The measure of the third angle is 28° less than 3 times the measure of the second angle. The sum of the angle measures of a triangle is 180°.

1) Define your variable. Write your equation and solve. (No justification necessary.)

2) What is the measure of the second angle?

3) What is the measure of the third angle?

Answer 1

1. Define your variable and write your equation: 36 + b + (3b-28) = 180°.
2. measure of the second angle: 43°.
3. measure of the third angle: 101°

Explanation:

a = 36

c = 3b - 28

a + b + c = 180°

a = measure of the first angle

b = measure of the second angle

c = measure of the third angle

then:

1) 36 + b + (3b-28) = 180 ⇒ )Define your variable. Write your equation and solve)

b + 3b + 36 - 28 = 180

4b + 8 = 180

4b = 180 - 8

4b = 172

b = 172/4

2) b = 43° ⇒ measure of the second angle

c = 3b - 28

c = 3*43 - 28

c = 129 - 28

3) c = 101° ⇒ measure of the third angle

Check:

36° + 43° + 101° = 180°