Question

an angle's measure is twice the measure of its complement. the larger angle is how many degrees greater than the smaller angle.

Answer 1

Two angles are complementary when they add up to 90 degrees

smaller angle = x
larger angle = 2x

x + 2x = 90
3x = 90
x = 90/3
x = 30°  ←  smaller angle 
larger angle = 2x = 2 * 30 = 60°

larger angle - smaller angle = 60° - 30° = 30°

The larger angle is 30 degrees greater than the smaller angle.