<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

Complementary Angles

Two angles that add to 90 degrees.

Atoms Practice
Estimated6 minsto complete
%
Progress
Practice Complementary Angles
 
 
 
MEMORY METER
This indicates how strong in your memory this concept is
Practice
Progress
Estimated6 minsto complete
%
Practice Now
Turn In
Complementary Angles

Complementary Angles

Two angles are complementary if they add up to 90. Complementary angles do not have to be congruent or adjacent.

What if you were given two angles of unknown size and were told they are complementary? How would you determine their angle measures?

Examples

Example 1

Find the measure of an angle that is complementary to ABC if mABC is 82.

9082=8.

Example 2

Find the measure of an angle that is complementary to ABCif mABC is 12

9012=78.

Example 3

The two angles below are complementary. mGHI=x. What is x?

Because the two angles are complementary, they add up to 90. Make an equation.

x+34x=90=56

Example 4

The two angles below are complementary. Find the measure of each angle.

The two angles add up to 90. Make an equation.

(8r+9)+(7r+6)=90(15r+15)=9015r=75r=5

However, you need to find each angle. Plug r back into each expression.

mGHImJKL=8(5)+9=49=7(5)+6=41

Example 5

Find the measure of an angle that is complementary to MRS if mMRS is 70.

Because complementary angles have to add up to 90, the other angle must be 9070=20.

Review

Find the measure of an angle that is complementary to ABC if mABC is:

  1. 4
  2. 89
  3. 54
  4. 32
  5. 27
  6. (x+y)
  7. z

Use the diagram below for exercises 8-9. Note that NK¯¯¯¯¯¯¯¯¯IL.

  1. Name two complementary angles.
  1. If mINJ=63, find mKNJ.

For 10-11, determine if the statement is true or false.

  1. Complementary angles add up to 180.
  2. Complementary angles are always 45.

Review (Answers)

To see the Review answers, open this PDF file and look for section 1.7. 

Resources

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Vocabulary

complementary angles

Two angles are complementary if they add up to 90^\circ.

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Complementary Angles.
Please wait...
Please wait...