Given:
Angles A and B are vertical angles.
The measure of angle A is 8x + 1 and angle B is 21 – 2x.
To find:
The measure of each angle.
Solution:
We know that vertically opposite angles are always equal.
Angles A and B are vertical angles.
[tex]m\angle A=m\angle B[/tex]
[tex]8x+1=21-2x[/tex]
Isolate variable terms.
[tex]8x+2x=21-1[/tex]
[tex]10x=20[/tex]
Divide both sides by 10.
[tex]x=\dfrac{20}{10}[/tex]
[tex]x=2[/tex]
Now,
[tex]m\angle A=8x+1[/tex]
[tex]m\angle A=8(2)+1[/tex]
[tex]m\angle A=16+1[/tex]
[tex]m\angle A=17[/tex]
And,
[tex]m\angle B=21-2x[/tex]
[tex]m\angle B=21-2(2)[/tex]
[tex]m\angle B=21-4[/tex]
[tex]m\angle B=17[/tex]
Therefore, the measure of angle A and angle B is 17 degrees.
