Question

∠A and ∠B\angle B ∠B are vertical angles. If m ∠A=(2x+7)∘\angle A=(2x+7)^{\circ} ∠A=(2x+7) ∘ and m ∠B=(5x+16)∘\angle B=(5x+16)^{\circ} ∠B=(5x+16) ∘ , then find the measure of ∠B\angle B ∠B.

Answer 1

The answer is below

Explanation:

An angle is defined as the figure formed by two rays meeting at a common end point. An angle is formed when two straight lines meet at a point. Angles are usually measured in degrees.

When two straight lines intersect, the pair of opposite angles formed is known as vertical angles (or vertical opposite angles). Vertical angles are equal to each other.

Given that ∠A and ∠B are vertical angles, therefore:

∠A = ∠B (vertical angles are equal)

2x + 7 = 5x + 16

2x - 5x = 16 - 7

-3x = 9

x = -3

∠B = 5x + 16

substituting x = -3:

∠B = 5(-3) + 16

∠B = -15 + 16

∠B = 1°