Question

The measure of the supplement of a angle is 12 more than twice the measure of the angle. What are the measures of the angle and its supplement?

Answer 1

The measure of the angle would be 56 degrees while the measure of its supplement would be 124.

Explanation:

To answer this question, one can start by writing an equation to model the situation. In this case, an equation that could model this problem is:

12+2a+a=180

Therefore, I chose to write this equation because supplement (or supplementary angles) are angles that add up to 180 degrees. Moreover, lets say the measure of one of the angles is represented by the letter a. Then the measure of the supplement could be represented by the expression 2a+12 (12 more than twice the measure of the angle).

Thus, by knowing all of this we can now write the equation I previously created. Which makes sense because if you add 2a+12 (the measure of the supplement) with "a" (the measure of the other angle) and put their sum to equal 180 it would be totally rational since the sum of supplementary angles add up to 180 degrees.

Now, all we have to do is solve.

12+2a+a=180
* minus 12
2a+a=168
3a=168
divide by 3
a=56
(measure of one of the angles)

Then we substitute for the value of a.

12+2a
12+2(56)
12+112
124 (measure of the supplement)

Finally, we check our answer.
56+124=180