Question

An angle measures 17 more than 3 times a number. A second angle is three more than 7 times the same number. The 2 angles are supplementary. What is the measure of each angle.

Answer 1

∠A = 65°

∠B = 115°

Explanation:

∠A = 3x + 17

∠B = 7x + 3

∠A + ∠B = 180

(3x + 17) + (7x + 3) = 180

10x = 160

x = 16

∠A = 16 x 3 + 17 = 65°

∠B = 16 x 7 + 3 = 115°

Answer 2

Answer: the angles are 65 degrees and 115 degrees.

Explanation:

Let x represent the number.

An angle measures 17 more than 3 times a number. This means that the angle is

3x + 17

A second angle is three more than 7 times the same number. This means that the second angle is

7x + 3

If two angles are supplementary, it means that their sum is 180 degrees. Therefore,

3x + 17 + 7x + 3 = 180

3x + 7x + 17 + 3 = 180

10x + 20 = 180

10x = 180 - 20

10x = 160

x = 160/10

x = 16

The first angle is

3 × 16 + 17 = 48 + 17 = 65 degrees

The second angle is

7 × 16 + 3 = 112 + 3 = 115 degrees