∠A and \angle B∠B are vertical angles. If m\angle A=(4x+8)^{\circ}∠A=(4x+8) ∘ and m\angle B=(5x-3)^{\circ}∠B=(5x−3) ∘ , then find the measure of \angle A∠A.

Answer 1

It's difficult to read what you typed for some reason but I think what you are saying is that:

Angle A equals 4x+8

Angle B equals 5x-b

and they are vertical angles.

If so, vertical angels are equal. You can set the expressions equal to each other, solve for x, and plug that value back in to solve for A.

4x+8=5x-b

add 3 to both sides

4x+11=5x

subtract 4x from both sides

11=x

Then plug x=11 into 4x+8.

4(11)+8

44+8

52

Angle A measures 52 degrees.

Answer 2

4x+8 = 5x-3 by the Vertical Angles Theorem that states the vertical angles are congruent.

Subtract 4x from both sides and get:

8=1x -3

Add 3 to both sides:

11= 1x

if x =11, plug that in to angle A.

4x+ 8 becomes 4(11)+8 =

44+ 8=

52