Complementary and Supplementary Angles - Trigonometry

According to the unit circle, an angle of is similar to an angle of .

Therefore:

Two angles that are supplementary add up to . For our problem, that means that .

Subtract from both sides.

In order for two angles to be complementary their sum must be , therefore the complementary angle can be found by subtracting the given angle from :

The sum of two complementary angles must be , therefore in order to determine the complementary angle of we simply subtract from as follows:

In order for two angles to be complementary their sum must equal , therefore we subtract the given angle from as follows:

However, it was stated that we are looking for the positive complementary angle, therefore, there is no positive complementary angle.

Two angles that are complementary must add to , therefore we subtract the given angle from as follows:

Two angles are complementary if their sum is , therefore we subtract the given angle from as follows:

Two angles are supplementary if their sum is , therefore we subtract the given angle from as follows:

Two angles are supplementary if their sum is , therefore we subtract the given angle from as follows:

If two angles are supplementary their sum is , therefore we subtract the given angle from as follows:

If two angles are supplementary their sum must be , therefore we subtract the given angle from to solve for the missing angle as follows:

For angles to be complement to each other, the two angle sets must sum to 90 degrees or radians.

Since all the sets of angles given add up to either of the two possibilites given, all of the angle sets are complement to each other.

The correct answer is:

All sets of angles given are complement to each other.

The supplementary angles must add up to 180 degrees.

In this case, to find the other angle supplementary to 15 degrees, simply subtract this angle from 180 degrees.

If is , that means that is either or . A complementary angle will add to with , so we can find what the complement is by subtracting our potential s from , or equivalently, :

Since all of the answer choices are positive, we want to see what the positive equivalent of this angle is. We can do this by adding , or equivalently :

This does not appear as an answer choice, but does.

To find the complement of , subtract it from , or equivalently, :

To find the supplement of , subtract it from , or equivalently :

In order to answer this question, we need to know that supplementary angles add together to be . We could use this to create an algebraic equation:

combine like terms

divide both sides by 2

We could also do this math mentally. If the angle plus itself equals , then we can divide by 2 to get .

Two angles are complementary if they add to . There are several ways of setting up this problem, but here is one. We can consider the angle we're looking for as "x."

If the angle we are looking for, x, is half its complement, that means that its complement is twice the angle, or 2x. We can then set up this equation to solve for x:

combine like terms

divide both sides by 3, or equivalently multiply by

There are many ways to solve this problem. Regardless, we need to know that supplementary angles add together to . To figure out what plus of itself would equal , we can set up this equation:

to combine like terms, create common denominators

multiply both sides by the reciprocal,

Our actual answer is going to be of this, since the angle that we are looking for is of its supplement. In other words, we just found x, and the angle that we are looking for is :

Our answer is .

Complementary angles add to .

Among the choices, this includes since

As a positive angle, this is .

It includes since

Supplementary angles add to .

Among the choices, this includes since

It also includes since which is coterminal with .

The one that doesn't work is since .