Question

Why are supplementary angles important?

Answer 1

Supplementary angles are important because they can be used to find other angles.

Explanation:

For example, if given the below problem and told that angle 1 equals 100˚, we could use supplementary angle that sum to 180 to determine all of the other angles.
Angles 1 and 2 are supplementary, so 180-angle 1 is equal to angle 2. Knowing angle to is therefore 80˚, we can continue using supplementary angles to find all other values.
Problems like this would not be possible without the proofs of supplementary angles.