Question

The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle.

Answer 1

Complementary angles signify that the two angles will add up to 90 degrees If the sum of your complementary angles exceeds the difference by 72, the equation will look like $x+y=x-y+72$, where x and y are the two different angles. You can cancel the x's out because they are on both sides, and you are left with the single variable equation, [text]y=-y+72[/tex], and when you solve for y, you find that y is 36 degrees, which means that x is 54 degrees. Since you want the smaller angle, 36 degrees would be correct.

Answer 2

Complementary angles add up to 90 degrees
x+y=90
(x+y)-(x-y)=72
x+y-x+y=72
2y=72
y=36
Replacing the value of x in the first equation;
x+36=90
x=90-36
x=54
The smaller angle is 36 degrees