<meta http-equiv="refresh" content="1; url=/nojavascript/"> Complementary Angles ( Read ) | Geometry | CK-12 Foundation
Dismiss
Skip Navigation
You are viewing an older version of this Concept. Go to the latest version.

Complementary Angles

%
Best Score
Practice Complementary Angles
Practice
Best Score
%
Practice Now
Complementary Angles
 0  0  0

What if you were given two angles of unknown size and were told they are complementary? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of complementary angles to solve problems like this one.

Watch This

CK-12 Complementary Angles

Watch this video beginning at around the 3:20 mark.

James Sousa: Angle Basics--Complementary Angles

Then watch the first part of this video.

James Sousa: Complementary Angles

Guidance

Two angles are complementary if they add up to 90^\circ . Complementary angles do not have to be congruent or next to each other .

Example A

The two angles below are complementary. m\angle GHI = x . What is x ?

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

x + 34^\circ & = 90^\circ\\x & = 56^\circ

Example B

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

The two angles add up to 90^\circ . Make an equation.

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

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

m \angle GHI & = 8(5^\circ) + 9^\circ = 49^\circ\\m\angle JKL & = 7(5^\circ) + 6^\circ = 41^\circ

Example C

Find the measure of an angle that is complementary to \angle MRS if  m\angle  MRS is  70^\circ .

Because complementary angles have to add up to 90^\circ , the other angle must be 90^\circ-70^\circ=20^\circ .

CK-12 Complementary Angles

Guided Practice

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

  1. 45^\circ
  2. 82^\circ
  3. 19^\circ
  4. 12^\circ

Answers:

  1. Because complementary angles have to add up to 90^\circ , the other angle must be 90^\circ-45^\circ=45^\circ .
  2. Because complementary angles have to add up to 90^\circ , the other angle must be 90^\circ-82^\circ=8^\circ .
  3. Because complementary angles have to add up to 90^\circ , the other angle must be 90^\circ-19^\circ=71^\circ .
  4. Because complementary angles have to add up to 90^\circ , the other angle must be 90^\circ-12^\circ=78^\circ .

Practice

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

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

Use the diagram below for exercises 8-9. Note that \overline{NK} \perp \overleftrightarrow{IL} .

  1. Name two complementary angles.
  1. If m\angle INJ = 63^\circ , find m\angle KNJ .

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

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

Image Attributions

Reviews

Email Verified
Well done! You've successfully verified the email address .
OK
Please wait...
Please wait...

Original text