College algebra

Question

Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180

degrees

°.

In a​ triangle, the measures of the three angles are​ x,

x plus 24

x+24​, and

x minus 36

x−36. What is the measure of each​ angle?

Answer 1

Hello Emily,

Create an equation based on the fact that the sum of the measures of the 3 angles in a triangle is 180:

x + x + 24 + x - 36 = 180

Add like terms: 3x - 12 = 180

Add 12 to both sides: 3x = 192

Divide both sides by 3: x = 64

Therefore:

1. Angle 1, x, has a measure of 64 degrees
2. Angle 2, x +24, has a measure of 88 degrees
3. Angle 3, x - 36, has a measure of 28 degrees

Check: Let's add all 3 angles: 64 + 88 + 28 = 152 + 28 = 180 degrees