Find the measure of an angle, if its supplement measures 20 degrees more than twice its complement

Question

Need to use the DVPES system to solve

Answer 1

I'm not sure what DVPES means, though I can guess about part of it.  However, this is probably close to it:

 

First define a variable.  Let x be the measure of the angle.

 

So the supplement is 180 - x, and the complement is 90 - x.

 

The statement says that 180 - x = 20 + 2 (90 - x).  That's an equation we can solve:

 

180 - x = 20 + 2 (90 - x)

 

Simplify:

180 - x = 20 + 180 - 2x

180 - x = 200 - 2x

 

Subtract 180 from both sides:

-x = 20 - 2x

 

Add 2x to both sides

x = 20

 

So the angle is 20 degrees.