Question

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

Answer 1

Answer:

∠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:

$x+y=180$

Insert the given values:

$x+(x-36)=180$

Solve for the value of x. Simplify parentheses:

$x+x-36=180$

Simplify addition:

$2x-36=180$

Add 36 to both sides:

$2x-36+36=180+36\\\\2x=216$

Isolate the variable. Divide both sides by 2:

$\frac{2x}{2}=\frac{216}{2}\\\\ x=108$

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

$x+y=180\\\\108+y=180$

Solve for y. Subtract 108 from both sides:

$108-108+y=180-108\\\\y=72$

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:

$108+72=180\\\\180=180$

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

$108-72=36\\36=36$

The given values are true.