Question

Suppose angle A and angle B are supplementary.

The measure of angle A is (15x + 65) and the measure of angle B is (50x - 15).

Solve for x (showing your setup and work) and then find the measure of angle A and the measure of angle B

Answer 1

x = 2

Angle A = 95°

Angle B = 85°

Explanation:

Concepts

Supplementary angles are angles that sum up to 180° to form a straight angle.

Application

We are asked to find the value of x, Angle A, and Angle B. We are given angles A and B as 15x + 65 and 50x - 15. To do this, we can set up the equation 15x + 65 + 50x - 15 = 180 because we know these angles are supplementary, or adding to 180°. Then, once we get the value of x, we plug in that value for each angle.

Solution

Step 1: Simplify both sides.

• 
  `(15x+50x) +(65-15)=180`
• 
  `65x+50=180`

Step 2: Subtract 50 from both sides.

• 
  `65x+50-50=180-50`
• 
  `65x=130`

Step 3: Divide both sides by 65.

• 
  `65x/65 = 130/65`
• 
  `x=2`

Step 4: Plug x into angle A.

• 
  `15(2)+65 = 30 + 65 = 95`

Step 5: Plug x into angle B.

• 
  `50(2) - 15 = 100 - 15 = 85`