Question

Find the measures of the complementary angles if the measure of the first angle is 40 degrees less than the measure of the second angle.

Answer 1

Let the measure of the second angle be $x$ degrees. Since the first angle is $40$ degrees less than the second angle, the measure of the first angle is $(x - 40)$ degrees. Since complementary angles add up to $90$ degrees, we have the equation $x + (x - 40) = 90$. Combining like terms gives $(2x - 40) = 90$. Adding $40$ to both sides gives $2x = 130$, and dividing by $2$ gives $x = \boxed{65}$ degrees. The first angle is $(x - 40)$ degrees $= (65 - 40)$ degrees $= \boxed{25}$ degrees.