Geometry · Triangles & polygons · 2.1

Triangle angle sum.

The three interior angles of ANY triangle always add up to 180°. Given two, subtract from 180° to find the third. With 50° and 60°, the third is 70°.

01 / THE IDEA

See it work.

The figure

See the shape.

50°60°?

Watch the method

Triangle angle sum

Third angle = 180 − (the other two).

1 / 2
1

Angle sum of a triangle

The three angles of any triangle add to 180°.

50∘+60∘+?=180∘50^\circ + 60^\circ + ? = 180^\circ
2

Subtract

Subtract the two known angles from 180°.

180−50−60=70∘180 - 50 - 60 = 70^\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.

180° every time

No matter the triangle’s shape, the angle sum is always 180°.

Why it works

Tear the corners — they form a straight line.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Two angles are 31° and 36°. Find the third.

1

Angle sum of a triangle

The three angles of any triangle add to 180°. 31° + 36° + ? = 180°

2

Subtract

Subtract the two known angles from 180°. 180 - 31 - 36 = 113°

EX 2medium

Two angles are 41° and 37°. Find the third.

1

Angle sum of a triangle

The three angles of any triangle add to 180°. 41° + 37° + ? = 180°

2

Subtract

Subtract the two known angles from 180°. 180 - 41 - 37 = 102°

EX 3hard

Two angles are 44° and 39°. Find the third.

1

Angle sum of a triangle

The three angles of any triangle add to 180°. 44° + 39° + ? = 180°

2

Subtract

Subtract the two known angles from 180°. 180 - 44 - 39 = 97°

04 / COMMON TRAPS

Where students slip.

Trap

Using 360°.

Fix

Triangles total 180°, not 360°.

Trap

Adding instead of subtracting.

Fix

Subtract the two known angles from 180°.

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

Two angles are 73° and 33°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
C2

Two angles are 72° and 44°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
C3

Two angles are 79° and 42°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
C4

Two angles are 62° and 72°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
Apply

Apply (4)

A1

Two angles are 71° and 68°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
A2

Two angles are 73° and 47°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
A3

Two angles are 70° and 63°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
A4

Two angles are 40° and 58°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
Extension

Extension (4)

E1

Two angles are 55° and 82°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
E2

Two angles are 59° and 45°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
E3

Two angles are 47° and 65°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.
E4

Two angles are 56° and 33°. Find the third.

Need a hint?
  • The angles add to 180°.
  • Subtract the two you know.