Question

The sum of the measures of two complementary angles exceeds the difference of their measure by 86º. Find the measure of each angle.

(For any of you who don't know, complementary means 2 angles that sum together to equal 90º)

Answer 1

let x represent first angle and y represent second angle. from condition of complementary angles we can write:

x+y = 90

now we can also write that:
x + y -86 = x - y
because our second condition is that their sum is greater than their difference by 86

solving second equation we get:
2y = 86
y = 43

second angle that is:
x = 90 - 43 = 47

Angles are 43 and 47 degrees.