The length of two complementary angles are x and 2x+12. Find the measures of the angles.

There's no such thing as the "length"of an angle.

But we know what you're getting at.

You have said that the angles are complementary. If two angles are

complementary, then their sum is 90 degrees, so we can take your

two angles and write:

x (one angle) plus (2x + 12) (the other one) = 90 degrees

x + 2x + 12 = 90

Subtract 12 from each side: x + 2x = 78

Add the x's on the left side: 3x = 78

Divide each side by 3 : x = 26 degrees

One angle is 'x' = 26 degrees

The other one is (2x + 12) = 52+12 = 64 degrees