SOLUTION: The measure of an angle’s supplement is 30 degrees more than three times the measure of its complement. What is the measure of the angle?

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Question 625538: The measure of an angle’s supplement is 30 degrees more than three times the measure of its complement. What is the measure of the angle?
Found 2 solutions by nerdybill, math-vortex:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
The measure of an angle’s supplement is 30 degrees more than three times the measure of its complement. What is the measure of the angle?
.
Let x = the angle
then
90-x = complement of angle
180-x = supplement of angle
.
From: "The measure of an angle’s supplement is 30 degrees more than three times the measure of its complement."
180-x = 3(90-x) + 30
180-x = 270-3x + 30
180-x = 300-3x
2x = 120
x = 60 degrees
Answer by math-vortex(648)   (Show Source): You can put this solution on YOUR website!
Hi, there-

The Problem:
The measure of an angle’s supplement is 30 degrees more than three times the measure of its
complement. What is the measure of the angle?

Solution:
Let x be the measure of the angle.

The angle's supplement is 180-x since the measures of an angle and its supplement add up to 
180 degrees.

The angle's complement is 90-x since the measures of an angle and its complement add up to
90 degrees.

We know that "the measure of an angle’s supplement is 30 degrees more than three times 
the measure of its complement." Translate this statement into an algebraic equation.

[the measure of an angle's supplement] = 30 + 3 * [the measure of its complement]
180-x = 30 + 3*(90-x)

Solve for x. First clear parentheses.
180-x = 30 + 270 - 3x

Combine the constant terms on the right 30+270 is 300.
180-x = 300 - 3x

Add 3x to both sides of the equation. On the left, -x+3x is 2x. On the right, -3x+3x=0
180+2x = 300 

Subtract 180 from both sides of the equation.
2x = 300-180
2x=120

Divide both sides by 2.
x=60.

The measure of the angle is 60 degrees.

Now check your work agains the information in the original problem.
The supplement of a 60 degree angle is 120 degrees since 60+120=180.
The complement of a 60 degree angle is 30 degrees since 60+30=90.
A 120 degree angle is 30 more than 3 times a 30 degree angle
120 is 30 more than 90. TRUE!

That's it. Please email your questions or comments. I'm happy to explain in more detail.

Ms.Figgy
math.in.the.vortex@gmail.com

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