Question

An angle is 10° more than the measure of its complement. Find the number of degrees in each angle. The angles measure degrees.

Answer 1

Let the angle be x.  The complement of this angle would then be 90-x.

We are told that x is 10 more than 90-x, or       x is 90-x+10, or x= 100 - x.

If x = 100 - x, then 2x = 100, and x = 50.

Check:  If one angle is 50 degrees, the complement is 90-50, or 40 degrees.

Are 50 and 40 complementary?  Yes.  They add up to 90.  Is 50 10 more than 40?  Yes.

The measurements of these two angles are 40 and 50 degrees.