# Complementary or Supplementary

To determine whether an angle pair is complementary or supplementary you have to recall the definition of complementary and supplementary.

Complementary - two angles whose sum is 90°

Supplementary - two angles whose sum is 180°

Example 1

Identify a pair of

m 1 = 40°

m 2 = 140°

m 3 = 50°

m 1 + m 3 = 90° therefore 1 and 3 are complementary.

m 1 + m 2 = 180° therefore 1 and 2 are supplementary.

Example 2: Determine if angles POQ and ROS are complementary or supplementary.

m POQ is 55°

m ROS is 35°

55° + 35° = 90° Therefore the angles are complementary.

Example 3: Identify a pair of complementary and a pair of supplementary angles.

m UTV is 20°

m VTW is 110°

m XYZ is 70°

m UTV + m XYZ = 20° + 70° = 90° UTV and XYZ are complementary

m VTW + m XYZ = 110° + 70° = 180° VTW and XYZ are supplementary

Example 4: Identify a pair of complementary and a pair of supplementary angles.

3 + 4 = 90°

1 + 2 = 90° + 90° = 180°

There are two methods to determining if an angle pair is complementary: (1) if you are looking at a diagram you will be looking for two adjacent angles that form a right angle.

(2) you can add the measure of any two angles and see if their sum is 90°.

There are two methods to determining if an angle pair is supplementary: (1) if you are looking at a diagram you will be looking for two adjacent angles that form a linear pair.

(2) you can add the measure of any two angles and see if their sum is 180°.

Complementary - two angles whose sum is 90°

Supplementary - two angles whose sum is 180°

Example 1

Identify a pair of

*complementary*and*supplementary*angles.m 1 = 40°

m 2 = 140°

m 3 = 50°

m 1 + m 3 = 90° therefore 1 and 3 are complementary.

m 1 + m 2 = 180° therefore 1 and 2 are supplementary.

Example 2: Determine if angles POQ and ROS are complementary or supplementary.

m POQ is 55°

m ROS is 35°

55° + 35° = 90° Therefore the angles are complementary.

Example 3: Identify a pair of complementary and a pair of supplementary angles.

m UTV is 20°

m VTW is 110°

m XYZ is 70°

m UTV + m XYZ = 20° + 70° = 90° UTV and XYZ are complementary

m VTW + m XYZ = 110° + 70° = 180° VTW and XYZ are supplementary

Example 4: Identify a pair of complementary and a pair of supplementary angles.

- 3 and 4 form a right angle. A right angle is 90° therefore they are complementary.

- 1 and 2 are a linear pair which means they are supplementary. m 1 = 90° and m 2 = 90°

*Quick Summary:*There are two methods to determining if an angle pair is complementary: (1) if you are looking at a diagram you will be looking for two adjacent angles that form a right angle.

(2) you can add the measure of any two angles and see if their sum is 90°.

There are two methods to determining if an angle pair is supplementary: (1) if you are looking at a diagram you will be looking for two adjacent angles that form a linear pair.

(2) you can add the measure of any two angles and see if their sum is 180°.

Related Links:Math Geometry Topics Polygons Supplementary Angles |

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