SOLUTION: angle DEF and angle FEG are complementary. m (angle) DEF= (3x-4), and m (angle) FEG= (5x+6) how do I find the measures of both angles?

Algebra ->  Angles -> SOLUTION: angle DEF and angle FEG are complementary. m (angle) DEF= (3x-4), and m (angle) FEG= (5x+6) how do I find the measures of both angles?      Log On


   

Question 360470: angle DEF and angle FEG are complementary. m (angle) DEF= (3x-4), and m (angle) FEG= (5x+6) how do I find the measures of both angles?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
since the angles are complementary, then the sum of both angles must equal 90 degrees.

you get:

(5x + 6) + (3x - 4) = 90

remove parenthese and combine like terms to get:

8x + 2 = 90

subtract 2 from both sides of the equation to get:

8x = 88

divide both sides of the equation to get:

x = 11

if x = 11, then:

angle 1 = 5x + 6 = 61 degrees

angle 2 = 3x - 4 = 29 degrees

sum of the angles is 90 degrees as it should be.

angle 1 = angle FEG

angle 2 = angle DEF

angle FEG = 61 degrees

angle DEF = 29 degrees