Two angles are supplementary. If and angle is 6 degrees more than twice the other angle, what are the angles?

Question

Two angles are supplementary. If and angle is 6 degrees more than twice the other angle, what are the angles?

Answer 1

If two angles are supplementary, then they add up to 180 degrees. We can call these two angles x and y.

 

x and y are supplementary, so x + y = 180.

 

If x is twice as big as y, plus 6, then x = 2y + 6

 

Because we know how much of y that x is equal to, we can replace x in the supplementary equation. So 180 = (2y + 6) + y .

 

Now that we only have one variable, y, in the equation, we can solve it using algebra.

 

180 = (2y + 6) + y 

Add the y's together

180 = 3y + 6

Subtract the 6 from 180

174 = 3y

Divide 174 by 3 to get y

58 = y

y = 58

 

Now we have a number for y, we can plug it into one of the first equations to get x. "x + y = 180" is simplest.

 

x + 58 = 180

x = 180 - 58

x = 122

 

We can use plug this number into the other equation to check the x and y solutions are correct.

 

x = 2y + 6

122 = 2y + 6

122 - 6 = 2y

116 = 2y

116/2 = y

58 = y

y = 58, again, so this is correct.

 

The two angles are 58 and 122 degrees. 

 

Hope this helps. Can you tell I don't have much to do until my own classes start next week?