Question

A and \angle B∠B are vertical angles. If m\angle A=(4x+23)^{\circ}∠A=(4x+23)

∘
and m\angle B=(5x-7)^{\circ}∠B=(5x−7)
∘
, then find the measure of \angle B∠B.

Answer 1

m∠B=143°

Explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always equal

so

In this problem we have that

m∠A=m∠B ----> by vertical angles

substitute the given values and solve for x

`(4x+23)=(5x-7)\\5x-4x=23+7\\x=30`

Find the measure of angle B

m∠B=(5x-7)°

substitute the value of x

m∠B=(5(30)-7)°

m∠B=143°