The measure of the supplement of an angle is 36 less than the measure of the angle. Find the measures of the angles.

Supplementary angles add up to

The angles are 72 and 108

Let the angles be x and y.

Such that:

So, we have:

--- sum of supplementary angles

Substitute

Collect like terms

Divide by 2

Recall that:

Hence, the angles are 72 and 108

See attachment for the illustration of the angles

Read more about supplementary angles at:

link

∠1 → 108

∠2 → 72

Step-by-step explanation:

Supplementary angles add up to a total of 180° (two angles is a pair). So:

∠1+∠2=180°

∠1 → supplement

∠2 → 36 less than the supplement

Create an equation, using x as angle 1 and y as angle 2:

Insert the given values:

Solve for the value of x. Simplify parentheses:

Simplify addition:

Add 36 to both sides:

Isolate the variable. Divide both sides by 2:

The value of x is 108. Insert this into the equation above:

Solve for y. Subtract 108 from both sides:

The value of y is 72.

Therefore:

∠1 → 108

∠2 → 72

:Done

*Check:

Insert the values into an equation set to 180 to determine if true:

Subtract 108 by 72 to see if the difference is 36:

The given values are true.