GED Math - Angle Geometry

Find the measure of angle B if it is the supplement to angle A:

$m\angle A=115^{o}$

$m\angle B=65^{o}$

$m\angle B=21^{o}$

$m\angle B=205^{o}$

$m\angle B=5^{o}$

Explanation

If two angles are supplementary, that means the sum of their degrees of measure will add up to 180. In order to find the measure of angle B, subtract angle A from 180 like shown:

$m\angle B=180^{o}-115^{o}=65^{o}$

This gives us a final answer of 65 degrees for angle B.

What is the measure of an angle supplementary to an $82^{\circ}$ angle?

$98^{\circ}$

$8^{\circ}$

$278^{\circ}$

$102^{\circ}$

No solution

Explanation

First we need to know that supplementary angles, when added, equal to $180^{\circ}$

So when we have the degree measurement of one angle, all we need to do is subtract it from the total (which is 180) and that will give us the measurement of our supplementary angle.

$180^{\circ}-82^{\circ}=98^{\circ}$

Find the the measure of angle B if it is complement of angle A:

$m\angle A=75^{o}$

$m\angle B=15^{o}$

$m\angle B=25^{o}$

$m\angle B=105^{o}$

$m\angle B=72^{o}$

Explanation

If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:

$m\angle B=90^{o}-75^{o}=15^{o}$

This gives us a final answer of 15 degrees for angle B.

In the figure above, $a\parallel b$ . If the measure of $\measuredangle 1=6x^{\circ}$ and $\measuredangle 6=4x^{\circ}$ , what is the measure of $\measuredangle8$ ?

$108^{\circ}$

$122^{\circ}$

$72^{\circ}$

$58^{\circ}$

Explanation

Since we have two parallel lines, we know that $\measuredangle1=\measuredangle4$ since they are opposite angle.

We also know that $\measuredangle 4 \text{ and }\measuredangle 6$ are supplementary because they are consecutive interior angles. Thus, we know that $\measuredangle 1$ is also supplementary to $\measuredangle6$ .

We can then set up the following equation to solve for .

Thus, $\measuredangle 1=108^{\circ}$ and $\measuredangle6=72^{\circ}$ .

Now, notice that $\measuredangle 8=\measuredangle 4$ because they are corresponding angles. Thus, $\measuredangle 8=\measuredangle 1=108^{\circ}$ .

In the figure above, $a\parallel b$ . If the measure of $\measuredangle 1=6x^{\circ}$ and $\measuredangle 6=4x^{\circ}$ , what is the measure of $\measuredangle8$ ?

$108^{\circ}$

$122^{\circ}$

$72^{\circ}$

$58^{\circ}$