Two angles are supplementary. The measure of the larger angle is 36 degrees more than twice the measure of the smaller angle. What is the measure of the smaller angle? Justify your answer.

The measure of the smaller angle under the given conditions in the question is; 48°

The sum of 2 supplementary angles by definition is equal to 180°.

Let the two angles be x and y.

Thus;

x + y = 180   (eq 1)

Now, we are told that the measure of the larger angle is 36 degrees more than twice the measure  of the smaller angle.

If the larger angle is x, then it means that;

x = 2y + 36

Put 2y + 36 for x in eq 1 to get;

2y + 36 + y = 180

3y + 36 = 180

3y = 180 - 36

3y = 144

y = 144/3

y = 48°

Thus;

x = 2(48) + 36

x = 96 + 36

x = 132°

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smaller angle=72°

larger angle= 180°-72°= 108°

i hope that this helps :)

Step-by-step explanation:

larger angle; 2x+36

supplementary is 180°

180°-36° = 144°

or 2x=144

x=144/2

x=72

smaller angle=72°

larger angle= 180°-72°= 108°