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# supplementry angles. i need help on this problem?

two angles are supplementry. one angle measures 12 degrees more than the other. find the measures of the angles

### 6 Answers

- 1 decade agoFavorite Answer
Okay. First, you need to know the definition of supplementary. This means, <x+<y=180degrees. (< stands for angle). So what you would do is, you would put what you know in an equation. You would then have...

(12 + x) + x= 180 degrees.

The reason why you are allowed to use two of the same variables is because they used the key words, "12 degrees more than the other" meaning that you can use the same variables.

You begin to solve the equation by first adding the common variables together. which is x. so your equation looks like:

2x + 12= 180 degrees.

you can now subtract 12 from 180 and you get 168. your equation now looks like.. 2x=168

Divide 168 by 2x and you end up with x=84. So one of your supplementary angles is 84 degrees. now to find the other angle, you simply have to add 12 to 84 and you get 96. So one angle is 96 degrees, while the other is 84 degrees.

A simple check.... 96+84=180 degrees! I hope you understand!

- 1 decade ago
To clarify:

x+y = 180

one angle is 12 degrees more than the other does not mean that you have an angle that is 162...

x = y+12

This means that x is 12 more than y

(y+12)+y = 180 This is substitution

2y + 12 = 180

2y = 168

y = 84

x+84=180 Substitution again

x=180 - 84

x = 96

(x,y)

(96,84)

One angle is 96 the other is 84.

- 1 decade ago
Supplementary angles means that they form a line, in other words, add up to 180 degrees.

So with that in mind, if one angle (x) is 12 degreees more than the other(y), ..your basic equation should be

x + y = 180 (They both have to add up to 180.

x = 12 + y (B/c angle x is 12 degrees more than angle y)

Those are your two equations. We know what X equals, so simply sub. that in for the X in the first equation. And then it's pretty nuch straight forward algebra.

(12 + y) + y = 180

12 + 2y = 180

y = 84

x + 84 = 180

x = 96.

So your two angle measures would be 96 & 84.

- 1 decade ago
Angle 1 = x

Angle 2 = x-12

(x)+(x-12) = 180

(x)+(x) = 192

2x = 192

x=96

Angle 1 = 96

Angle 2 = 96 - 12 = 84

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