Question

Find the measures of two supplementary angles if three times the measure of one angle is 12 degrees less than the measure of the other

Answer 1

Answer: 42° and 138°

Step-by-step explanation: If two angles are supplementary, then the sum of their measures is 180°.

In this problem, since we don't know the measures of our supplementary angles, let's call the first angle X. If an angle measures X°, then the measure of its supplement is 180 - X degrees.

So let's call X an angle and 180 - X its supplement.

Now to find the value of X, we can use the second part of the problem to set up an equation. "Three times the measure of one angle" that's 3x, "is" means equals, "12 degrees less than the measure of the other" would be 180 - X - 12.

3x = 180 - x - 12

Now we can solve for X by first simplifying on the right side by subtracting 12 from 180 and we have 3x = 168 - x. Now we add X to both sides of the equation and we get 4x = 168. Now we divide both sides of the equation by 4 in order to get X by itself. Diving both sides by 4, we find that X = 42.

So the measure of one angle which is X is 42°. The measure of its supplement which is 180 - 42 is 138°.

Answer 2

42 and 138

Explanation:

Supplementary angle mean that the sum of both angle will be 180 degrees. If the angle is X and Y the equation will be:

x + y = 180

x= 180-y

If three times the measure of one angle(X) is 12 degrees less than the measure of the other(Y), the equation will be

3x= y-12

If you insert first equation to second equation, you can find out:

3x= y-12

3(180-y)= y-12

540-3y= y-12

540+12= y+3y

552= 4y

y= 138

x=180- y

x= 180-138

x= 42