Trick question?

Suppose m<A=77 degrees. What is the measure of a complement of a complement <A? Explain.

a complement of angle 77 is 13 degrees. but a complement of a complement wouldn't that be 77?? Help!!

No, it's not a trick question. Let's break it down step by step to understand the concept of a complement and a complement of a complement.

First, let's define what a complement is. In geometry, the complement of an angle is another angle that, when added to the original angle, equals 90 degrees. This means that if angle A measures 77 degrees, its complement angle B will measure:

B = 90 - A
B = 90 - 77
B = 13 degrees

Now, let's move on to understanding the complement of a complement. The complement of an angle is an angle that, when added to the original angle, equals 90 degrees. In this case, the complement of angle B (which is 13 degrees) will be:

C = 90 - B
C = 90 - 13
C = 77 degrees

So, the measure of the complement of a complement of angle A is 77 degrees, not 13 degrees. The complement of a complement brings us back to the original angle. This is an important property of complements in geometry.

To find the measure of a complement of a complement, you can use the following formula:

Angle 1:
Given angle A = 77 degrees

Complement of angle 1:
Angle 2 = 90 - Angle 1
Angle 2 = 90 - 77
Angle 2 = 13 degrees

Complement of a complement of angle 1:
Angle 3 = 90 - Angle 2
Angle 3 = 90 - 13
Angle 3 = 77 degrees

I hope this explanation clarifies the concept for you.

The same as the supplement of a supplement :)