Two angles are supplementary if their sum is 180°. The larger angle measures thirty degrees more than twice the measure of a smaller angle. If x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.

Answer: This small angle is 50°.

The larger angle is 130°

Step-by-step explanation:

Let x represent the measure of the smaller angle.

The larger angle measures thirty degrees more than twice the measure of a smaller angle. This means that the measure of the larger angle is

2x + 30

Two angles are supplementary if their sum is 180°. If the two angles are supplementary, it means that

x + 2x + 30 = 180

3x + 30 = 180

3x = 180 - 30

3x = 150

x = 150/3

x = 50

The measure of the larger angle is

2x + 30 = 2 * 50 + 30

= 130°

30 + 2x = 180

2x = 150

x = 75

So the smaller angle is 75 degrees

and the larger angle is said to be 30 more than the smaller so,

75 + 30 = 105 degrees

Larger angle = 105 degrees

Smaller angle = 75 degrees