Question 1160070: An angle measures 83.6° more than the measure of its complementary angle. What is the measure of each angle?
Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! if the angles are complementary, then their sum is 90 degrees.
let x = the angle.
let y = the complementary angle.
x + y = 90
the angle measures 83.6 degrees more than its complement.
x = y + 83.6
replace x in the equation of x + y = 90 to get:
y + 83.6 + y = 90
combine like terms to get:
2y + 83.6 = 90
subtract 83.6 from both sides of the equation to get:
2y = 90 - 83.6
combine like terms to get:
2y = 6.4
solve for y to get:
y = 3.2
you have:
y = 3.2
x = y + 83.6 which makes x = 3.2 + 83.6 = 86.8
x + y = 90 becomes 86.8 + 3.2 = 90 which becomes 90 = 90
this confirms the solution is correct.
the solution is:
the angle is 86.8 degrees and its complement is 3.2 degrees.
Let angle be A
Then its complement is: 90 - A
We then get: A = 90 - A + 83.6
A + A = 90 + 83.6
2A = 173.6
Angle, or
Can you now find the complementary angle?