# How do you use algebra to solve problems concerning angles? Two angles are supplementary and the degree measure of one of the angle in 30 less than twice the degree measure of the other. Find...

How do you use algebra to solve problems concerning angles?

Two angles are supplementary and the degree measure of one of the angle in 30 less than twice the degree measure of the other. Find the degree measure of each angle.

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Two angles x, y are complementary if their sum is 90 degrees and they are supplementary if their sum is 180 degrees.

For the problem given let one of the angles be x, the other angle y = 2x - 30. As the angles are *supplementary* 2x - 30 + x = 180

=> 3x = 210

=> x = 70

**The angles are 70 degrees and 110 degrees.**

First of all, the angles must either equate each other or equate another number.

Complementary angles add up to 90 degrees.

Let the first angle be x and the second y.

The first number is 30 less than twice the other angle

This means: x= 2y-30

BUT x+y=90 degrees.

To solve the equation, substitute x=2y-30 for y in

x+y=90

(2y-30)+y=90

2y+y-30=90

3y-30=90

collect like terms

3y=90+30

3y=120

divide both sides by 3

y=40 degrees.

since y=40,

then x=2y-30= 2(40)-30=80-30=50 degrees.

Therefore, the angles are 50 degrees and 40 degrees.