Geometry · Angles · 1.2

Complementary angles.

Two angles are complementary when they add up to 90°. To find the missing one, subtract the known angle from 90°. The complement of 35° is 55°.

01 / THE IDEA

See it work.

The figure

See the shape.

35°

Watch the method

Complementary angles

Complement of a° = 90 − a.

1 / 2
1

Complementary angles

Two angles are complementary when they add to 90°.

?+35∘=90∘? + 35^\circ = 90^\circ
2

Subtract

Subtract the known angle from 90°.

90−35=55∘90 - 35 = 55^\circ
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Find the measure.

Type the number — units optional.

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

Make a right angle

Together complementary angles form a right angle, so they total 90°.

Why it works

Two pieces of a corner.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the complement of 45°.

1

Complementary angles

Two angles are complementary when they add to 90°. ? + 45° = 90°

2

Subtract

Subtract the known angle from 90°. 90 - 45 = 45°

EX 2medium

Find the complement of 72°.

1

Complementary angles

Two angles are complementary when they add to 90°. ? + 72° = 90°

2

Subtract

Subtract the known angle from 90°. 90 - 72 = 18°

EX 3hard

Find the complement of 36°.

1

Complementary angles

Two angles are complementary when they add to 90°. ? + 36° = 90°

2

Subtract

Subtract the known angle from 90°. 90 - 36 = 54°

04 / COMMON TRAPS

Where students slip.

Trap

Using 180° instead of 90°.

Fix

Complementary is 90°; supplementary is 180°.

Trap

Forgetting to subtract.

Fix

Subtract the known angle from 90°.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Find the complement of 77°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
C2

Find the complement of 46°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
C3

Find the complement of 33°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
C4

Find the complement of 60°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
Apply

Apply (4)

A1

Find the complement of 55°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
A2

Find the complement of 71°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
A3

Find the complement of 13°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
A4

Find the complement of 20°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
Extension

Extension (4)

E1

Find the complement of 21°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
E2

Find the complement of 36°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
E3

Find the complement of 78°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.
E4

Find the complement of 57°.

Need a hint?
  • Complementary angles add to 90°.
  • Subtract from 90°.