# GED Math : Complementary Angles

## Example Questions

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### Example Question #1 : Complementary Angles

Refer to the above figure. You are given that .

Which two angles must be complementary?

and

and

and

and

and

Explanation:

and  form a linear pair, so their measures add up to that of a straight angle, which is . They must be supplementary (and cannot be complementary).

and  are a pair of vertical angles - angles formed from a pair of intersecting lines which together have the lines as the union. They must be congruent, and need not be complementary.

and  are a pair of same-side interior angles formed by transversal  across the parallel lines. They must be supplementary (and cannot be complementary).

and  are the acute angles of right triangle . They must be complementary. This is the correct pair.

### Example Question #1 : Complementary Angles

Angles A and B are complementary angles. The measure of angle A is , The measure of Angle B is . find the value of .

Explanation:

Since angles A and B are complementary, their measures add up to 90 degrees. Therefore we can set up our equation as such:

-or-

Combine like terms and solve for :

### Example Question #2 : Complementary Angles

What is the measure of an angle that is complementary to an angle measuring ?

Explanation:

The sum of complementary angles is equal to

Set up the following equation and solve for :

### Example Question #3 : Complementary Angles

Angles A and B are complementary angles. The measure of angle A is . The measure of angle B is . Solve for .

Explanation:

Since angles A and B are complementary angles, their measurements add up to equal 90. Therefore, we need to set up our equation as follows:

-or-

Combine like terms:

And solve for :

### Example Question #4 : Angle Geometry

Angles A and B are complementary angles. The measure of angle A is . The measure of angle B is . What are the measures of the two angles?

No solution

Explanation:

Since angles A and B are complementary, their measures add up to equal 90 degrees. Therefore we can set up an equation as follows:

-or-

Combine like terms and solve for :

Now that we have found , we need to plug that back in to the two angle measurements

### Example Question #4 : Complementary Angles

What angle is complementary to 55?

Explanation:

The definition of a complementary angle means that two angles must add up to 90 degrees.

To find the angle, simply subtract 55 from 90.

### Example Question #5 : Complementary Angles

What angle is complementary to 10 degrees?

Explanation:

Complementary angles must add up to ninety.

Subtract the given angle from 90 to find the other angle.

### Example Question #6 : Complementary Angles

Suppose the angles  and  are complementary angles.  What is the value of ?

Explanation:

Set up the equation such that both angles sum up to 90.

Divide both sides by 8.

The value of  is:

### Example Question #7 : Complementary Angles

Determine the value of  if the angles  and  are complementary.

Explanation:

Complementary angles must add up to 90 degrees.

Set up an equation so that the sum of two angles add up to 90.

Subtract 8 on both sides.

Simplify both sides.

Divide by two on both sides.

### Example Question #8 : Complementary Angles

What angle is complementary to  radians?

Explanation:

Note that this is in radians.  Recall that 2 complementary angles must add up to 90 degrees.

Since ,

To find the complementary angle, subtract  from .