Question

Angle A and angle B are supplementary.The measure of angle B is 15∘ less than the measure of angle A.What is the measure of angle B, in degrees?

Answer 1

Angle A and B are supplementary meaning they add up to 180 degrees. By setting up an equation and substituting B with (A - 15), we find that angle B measures 82.5 degrees.

Step-by-step explanation:

The measure of angle B is 15 degrees less than angle A, so we can express it as (A - 15) degrees.

Angle A and angle B are supplementary angles which means their measures add up to 180 degrees. If angle B is 15 degrees less than angle A, we can set up the equation A + B = 180 degrees and substitute B with (A - 15) since B is 15 degrees less than A. This gives us A + (A - 15) = 180 degrees.

Solving the equation for A gives us:

1. 2A - 15 = 180
2. 2A = 195
3. A = 97.5

Now, we can find angle B:

1. B = A - 15
2. B = 97.5 - 15
3. B = 82.5 degrees

Therefore, the measure of angle B is 82.5 degrees.

Answer 2

The answer to your question is B = 82.5°

Step-by-step explanation:

Data

A and B are supplementary angles

A = x

B = x - 15°

Process

1.- Write and equation to solve this problem. As these angles are supplementary the sum equals 180°.

A + B = 180°

2.- Substitution

x + x - 15 = 180

3.- Solve for x

2x = 180 + 15

2x = 195

x = 195 / 2

x = 97.5

4.- Find the measure of angle B

B = x - 15

B = 97.5 - 15

B = 82.5°