An angle measures $$ 82^{\circ} $$ more than the measure of its supplementary angle. What is the measure of each angle? $$ \square^{\circ} \text { and } \square^{\circ} $$

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UpStudy AI · Accepted Answer

Let the measure of the angle be $$ x $$ degrees. The supplementary angle, which is the angle that adds up to $$ 180^\circ $$ with $$ x $$, can be expressed as $$ 180^\circ - x $$.

According to the problem, the angle $$ x $$ measures $$ 82^\circ $$ more than its supplementary angle. We can set up the equation:

$$
x = (180^\circ - x) + 82^\circ
$$

Now, simplify the equation:

$$
x = 180^\circ - x + 82^\circ
$$

Combine like terms:

$$
x = 262^\circ - x
$$

Now, add $$ x $$ to both sides:

$$
x + x = 262^\circ
$$

This simplifies to:

$$
2x = 262^\circ
$$

Now, divide both sides by 2:

$$
x = 131^\circ
$$

Now, we can find the measure of the supplementary angle:

$$
180^\circ - x = 180^\circ - 131^\circ = 49^\circ
$$

Thus, the measures of the angles are:

$$
\boxed{131^\circ} \text{ and } \boxed{49^\circ}
$$
The measures of the angles are $$ 131^\circ $$ and $$ 49^\circ $$.

An angle measures more than the
measure of its supplementary angle. What
is the measure of each angle?

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An angle measures more than the measure of its supplementary angle. What is the measure of each angle?