Question

∠A and ∠B are supplementary angles. If m∠A = (8x+6)° and m∠B = (7x+24)°, then find the measure of ∠B.

A) 8°
B) 15°
C) 38°
D) 46°

Answer 1

To find the measure of angle B, we set up the equation (8x+6)° + (7x+24)° = 180° and solve for x. Once we find the value of x, we substitute it back into the equation to find the measure of angle B. The answer is 94°, so Option D) 46° is correct.

Step-by-step explanation:

To find the measure of angle B, we need to know that the sum of supplementary angles is 180 degrees. So, we can set up the equation:

(8x+6)° + (7x+24)° = 180°

Combine like terms:

15x + 30 = 180

Subtract 30 from both sides:

15x = 150

Divide by 15:

x = 10

Now, substitute x back into the equation to find the measure of angle B:

m∠B = (7x+24)° = (7(10)+24)° = 94°.

Therefore, the measure of angle B is 94°, so the answer is Option D) 46°.