Angle Terminology with Equations

Question

what is the correct answer to this problem ∠A and \angle B∠B are vertical angles. If m\angle A=(2x+29)^{\circ}∠A=(2x+29)

∘

and m\angle B=(3x-17)^{\circ}∠B=(3x−17)

∘

, then find the measure of \angle B∠B.

Answer 1

If angles A and B are vertical angles, then it is assumed that they are congruent angles (they have the same measure. We can use the information given to solve for x first.

∠A = 2x + 29

∠B = 3x - 17

2x + 29 = 3x - 17

-2x -2x

29 = x - 17

+17 +17

x = 46

Now, they want to know the measure of ∠B, so plug the value of x into that expression (3x - 17) and you will get your answer.

m∠B = 3x - 17 = 3(46) - 17 = 138 - 17 = 121º

Since they are vertical angles, that will also be the measure of ∠A

m∠B = 2x + 29 = 2(46) + 29 = 92 + 29 = 121º