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

let the angle be x

then its complement is 90-x

It says : x = 2(90-x)

solve for x

x=60

To solve this problem, we need to first understand what a complement of an angle is.

The complement of an angle is the angle that, when added to the original angle, gives a sum of 90 degrees. For example, if the angle is x degrees, then its complement is (90 - x) degrees.

Now, let's represent the smaller angle as x degrees. The problem states that the larger angle is twice the measure of its complement, which means the larger angle is 2 times (90 - x) degrees.

To find the difference between the larger and smaller angles, we subtract the measure of the smaller angle from the larger angle:

Difference = Larger angle - Smaller angle
Difference = (2 times (90 - x)) degrees - x degrees

We simplify the expression:

Difference = 180 degrees - 2x degrees - x degrees
Difference = 180 degrees - 3x degrees

So, the larger angle is 180 - 3x degrees greater than the smaller angle.