The measures of two supplementary angles are (4x + 8) and (6x + 3) º.

What is the measure of the smaller angle?

OA. 23.6°

OB. 62.6°

C. 104.4°

OD. 75.6°

OD. 75.6°

Step-by-step explanation:

Given:

Two supplementary angles (4x + 8) and (6x + 3)

Solve x:

(4x + 8) + (6x + 3) = 180

4x + 8 + 6x + 3 = 180

10x + 11 = 180

10x = 169

x = 16.9

Find the two angles:

4x + 8 = 4 (16.9) + 8 = 75.6°

6x + 3 = 6 (16.9) + 3 = 104.4°

smaller angle = 75.6°

Check:

75.6° + 104.4° = 180°

Step-by-step explanation:

A supplementary angle is an angle that is 180 degrees. We are given two angles that add up to 180, but we need to solve for x first.

The first step is to solve both angles. We know that both angles added together are supplementary, so they are equal to 180.

4x + 8 = unknown angle

6x + 3 = unknown angle

(4x + 8) + (6x + 3) = 180

Because we know a supplementary angle is 180 degrees, we can solve for x to find both angles.

Solve for x.

(4x + 8) + (6x + 3) = 180

10x + 11 = 180

10x = 169

x = 16.9

Now, we know the value of x, so we plug in x for both angles to determine which angle is smaller.

4x + 8

4 (16.9) + 8

67.6 + 8 = 75.6 degrees

and the other angle

6x + 3

6 (16.9) + 3

101.4 + 3 = 104.4 degrees

Now we know that the smaller angle is 75.6 degrees.

Also, to make sure the math is correct, when plugging in both numbers after finding x, they should add to 180.

75.6 + 104.4 = 180 so we know they are supplementary for sure.

Good luck!