Question

One angle measures 54 more degrees than 3 times another angle. The angles are supplementary. What are their measures?

Answer 1

Another angle: α
Three times another angle 3α
54 degrees more: +54°

The one angle: 3α + 54°

Angles are supplementary, so: α + 3α+54° = 180°
4α = 180° - 54°
4α = 126°
4α :4 = 126° :4
another angle: α = 31.5°

The one angle: 3·31.5° + 54° = 94.5 + 54° = 148.5°

The maesures of angles are: 31.5° and 148.5°

Answer 2

Let one of the angle be x,

The other is = 3x + 54

If angles are supplementary it means they both add up to 180°

Therefore: x + (3x + 54) = 180

x + 3x + 54 = 180

4x + 54 = 180

4x = 180 - 54

4x = 126

x = 126/4 = 31.5

So the angles are x, (x + 54) = 31.5, (31.5 + 54) = 85.5

Measures of angles are 31.5° and 85.5°