# The measure of the supplement of an angle is 20° more than three times the measure of the original angle. What are the measures of the angles?

Feb 27, 2017

The original angle is ${40}^{\circ}$.
Its supplement is ${140}^{\circ}$

#### Explanation:

Recall that the sum of supplemental angles is ${180}^{\circ}$.

Based on the question, an expression can be set up with a variable.

If $x$ is the value of the original angle, and $\left(3 x + 20\right)$ is equal to its supplement, then
$180 = x + \left(3 x + 20\right)$

Solving for x, we get:
$180 = 4 x + 20$

$160 = 4 x$

$40 = x$

The original angle is ${40}^{\circ}$.

To find the supplement, plug in 40 to the expression that we defined above. The supplement is equal to:
$= 3 \cdot \left(40\right) + 20$

$= 120 + 20 = 140$

Its supplement is ${140}^{\circ}$

To check, verify that the two angle measurements meet the definition, meaning they sum to ${180}^{\circ}$

${140}^{\circ} + {40}^{\circ} = {180}^{\circ}$