7th Grade - Complementary & Supplementary Angles

Introduction

  • The sum of two angles defines complementary and supplementary angles.

Complementary Angles

  • Two acute angles form complementary angles.
  • The sum of these two angle measures is 90o (right angle).
  • Each angle complements the other.
  • In the diagram shown below, mXOY+mYOZ = 90°, and hence they are complementary angles.

  • Complementary angles do not have to be always adjacent angles. For example, AOB and CDE shown below are not adjacent angles, but still, they are complementary angles.

                                   

Supplementary Angles

  • Two angles are said to be supplementary if their sum measures 180°.
  • In other words, two angles that form a line are called supplementary angles.
  • Each angle supplements the other angle.
  • In the diagram shown below, mAOB + mBOC = 180°, and hence they are a pair of supplementary angles.

  • Supplementary angles do not have to be always adjacent angles. For example, XYZ and MOP shown below are not adjacent angles, but still, they are supplementary angles.

 

Solved Examples

Question1: Find the measures of ABC and XYZ if they are complementary.

Solution: The sum of two complementary angles is 90°.

ABC+XYZ=90°

x4+x5=90°

9x20=90°

x=90°×209

x=200°

ABC=x4=200°4=50°

XYZ=x5=200°5=40°

Question 2: The difference between two supplementary angles is 20 degrees. Find the measure of both angles.

Solution: Let one of the angles be x°. Then, the other angle will be 180-x°.

According to the question:

180-x°-x°=20°

180°-2x°=20°

2x°=180°-20°

2x°=160°

x°=160°2=80°

So, one angle is 80°. Then, the other angle will be 100°.

Cheat Sheet

  • Complementary Angles:
    • Two angles are said to be complementary if their sum is 90°.
    • The complement of an angle x° is 90-x°.
  • Supplementary Angles:
    • Two angles are said to be supplementary if their sum is 180°.
    • The supplement of an angle y° is 180-y°.

Blunder Areas

  • Two angles that add up to 90° are complementary angles. Both angles are not necessarily adjacent.
  • Two angles that add up to 180° are supplementary angles. Both angles are not necessarily adjacent.