Question

Two angles are supplementary. The measure of the larger angle is 36 more than the measure of the smaller angle. Find their measures.

the answers are 72° and 108° but I need help showing my work​

Answer 1

Explanation:

let the smaller angle be x

then the measure of larger angle will be x+36

x+x+36=180°(being supplementary angle)

2x+36=180°

2x=180°-36

2x=144°

x=144°/2

x=72°

now,

the larger angle x+36 = 72+36=108°

Answer 2

x = smaller angle

x+36 = larger angle, since its 36 degrees more than the smaller angle

The two angles x and x+36 must add to 180 if they are to be supplementary (aka form a straight line)

So this means we can say the following:

(smaller)+(larger) = 180

(x) + (x+36) = 180

2x+36 = 180

2x = 180-36

2x = 144

x = 144/2

x = 72 is the smaller angle

x+36 = 72+36 = 108 is the larger angle

As a check:

smaller+larger = 72+108 = 180

which shows they are supplementary and it confirms our answers