Question

an angle measures 58.4° more than the measure of its supplementary angle what is the measure of each angle

Answer 1

60.8° and 119.2°

Explanation:

α - smaller angle

β = α + 58,4° - larger angle

The sum of supplementary angles is 180°.

Therefore:

α + β = 180°

α + α + 58.4° = 180°

2α = 180° - 58.4°

2α = 121.6°

α = 121.6°÷2 = 60.8°

β = 60.8° + 58.4° = 119.2°

Checking: 119.2° + 60.8° = 180°

Answer 2

58.4

119.2

Explanation:

Givens

Let one angle = x

Let the other angle = x + 58.4

Together they make 180 degrees.

Equation

x + x + 58.4 = 180 Collect like terms.

Solution

2x + 58.4 = 180 Subtract 58.4 from both sides

2x = 180 - 58.4

2x = 121.6 Divide by 2

x = 60.8

Answer

x = 60.8

x + 58.4 = 119.2