Question

Angles A and B are vertical angles. The measure of angle A is 8x + 1 and angle B is 21 – 2x. Find each angle measure.

Answer 1

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.

$m\angle A=m\angle B$

$8x+1=21-2x$

Isolate variable terms.

$8x+2x=21-1$

$10x=20$

Divide both sides by 10.

$x=\dfrac{20}{10}$

$x=2$

Now,

$m\angle A=8x+1$

$m\angle A=8(2)+1$

$m\angle A=16+1$

$m\angle A=17$

And,

$m\angle B=21-2x$

$m\angle B=21-2(2)$

$m\angle B=21-4$

$m\angle B=17$

Therefore, the measure of angle A and angle B is 17 degrees.