Complementary, supplementary and vertical angles

About this lesson

Grade 7 › Angles, triangles and prisms

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Complementary, supplementary and vertical angles

Warm-up

Three quick questions from earlier lessons.

Discover

Two angles sit side by side on a straight line. One is 130∘130^\circ. What is the other?

  1. 50∘50^\circ
  2. −40∘-40^\circ

Key idea

Angle facts give equations.

Complementary angles add to 90∘90^\circ; supplementary angles add to 180∘180^\circ (angles on a straight line). Vertical angles (opposite at a crossing) are equal. Write an equation and solve for the unknown.

Worked example

Angles 2x∘2x^\circ and 40∘40^\circ are complementary.

2x+40=902x + 40 = 90
Add to 90.
x=25x = 25
Solve.

Your turn, guided

Your turn: the supplement of 72∘72^\circ.

108108
180 − 72.

Practice ★

  1. An angle measures 33∘33^\circ. What is its complement (degrees)?
  2. An angle measures 61∘61^\circ. What is its complement (degrees)?
  1. An angle measures 81∘81^\circ. What is its supplement (degrees)?

Watch out!

Practice ★★

  1. Two angles on a straight line measure 68∘68^\circ and (x+22)∘(x + 22)^\circ. Find xx.
  2. Two angles on a straight line measure 34∘34^\circ and (x+9)∘(x + 9)^\circ. Find xx.

Exit ticket

Three questions to check you have got it.

  1. An angle measures 33∘33^\circ. What is its complement (degrees)?
  2. An angle measures 61∘61^\circ. What is its complement (degrees)?
  3. An angle measures 39∘39^\circ. What is its complement (degrees)?

Summary card

Angle relationships

Complementary: 90°. Supplementary: 180°. Vertical: equal.

Watch out: complement 90, supplement 180.

End of the lesson

Next lesson: Building triangles: the triangle inequality Back to the chapter

Answers: Complementary, supplementary and vertical angles

A

  1. 5757
  2. 2929

B

  1. 9999

C

  1. 9090
  2. 137137

D

  1. 5757
  2. 2929
  3. 5151

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