Question

A and B are supplementary angles. If m∠A = (8x – 25)º and m∠B = (7x - 5)º, then find the measure of ∠B.

a) 140º
b) 120º
c) 100º
d) 80º

Answer 1

To find the measure of ∠B, set up an equation for supplementary angles, solve for x, and then substitute x back into the expression for ∠B. Upon solving, the measure of ∠B is found to be 93°, which does not match any of the given options.

Step-by-step explanation:

The question asks us to find the measure of ∠B, given that A and B are supplementary angles, and the measures of ∠A and ∠B are given as algebraic expressions. Supplementary angles add up to 180°. Therefore, we can set up an equation (8x - 25) + (7x - 5) = 180 and solve for x. After finding the value of x, we substitute it back into the expression for ∠B (7x - 5) to find its measure.

Step-by-step solution:

1. Set up the equation for supplementary angles: (8x - 25) + (7x - 5) = 180.
2. Solve for x: 15x - 30 = 180.
3. Add 30 to both sides: 15x = 210.
4. Divide by 15 to find x: x = 14.
5. Substitute x back into the expression for ∠B: m∠B = (7×14) - 5.
6. Calculate m∠B: m∠B = 98 - 5.
7. Find the measure of ∠B: m∠B = 93°.

The measure of ∠B is 93°, which is not one of the provided options, indicating a potential typo or mistake in the question or answer choices.