Sum of angles in a triangle

Type two angles in degrees. The sum in a triangle is 180°, so the third is 180° minus those two. 60° and 60° give 60°. 90° and 45° give 45°. 30° and 70° give 80°.

The calculator subtracts α and β from 180. It does not check that the sum is smaller than 180. 100° and 90° give −10, because that is the formula.

Input data

Results

Enter data and click Calculate.

How it works

In a plane triangle the three angles add to 180°. You know two, the third is the remainder. 60° and 60° leave 60°, equilateral. 90° and 45° leave 45°, a right isosceles.

The fields are α and β in degrees. The calculator computes 180 − α − β. 30° and 70° give 80°. Order does not change the sum: 70° and 30° also give 80°.

When the two already exceed 180°, the result is negative. 100° and 90° give −10. That is not a new kind of triangle, only the same formula with no lock. On paper that drawing does not close.

The laws of sines and cosines find sides. There is no side here. Only two angles and the rest to 180°.

The header units switch does not multiply anything. 60 and 60 stay 60 whatever the label says.

60° and 60° give 60°. 90° and 45° give 45°. 30° and 70° give 80°. 120° and 30° give 30°.

Formula

γ = 180° − α − β

How to use

  1. Type two angles, for example 60 and 60.
  2. Click Calculate. The third is 60°.
  3. 90° and 45° give 45°. 30° and 70° give 80°.
  4. A sum larger than 180° gives a minus. On paper that is not a triangle.
  5. A side from angles lives on the law of sines. Here you stay with the third angle.

60° and 60° give 60°

γ = 180° − α − β. 60° and 60° give 60°. 90° and 45° give 45°. 30° and 70° give 80°.

sum
α + β + γ = 180° in the plane. Two angles leave the rest. 60 and 60 leave 60.
α
The first known angle. 90° with 45° leaves 45°. 30° with 70° leaves 80°.
β
The second known angle. Order with α does not change the third. A sum over 180° gives a minus.

Examples

Example 1

  • α = 60°
  • β = 60°

60

What is the third angle with 60° and 60°? 60°. Equilateral.

Example 2

  • α = 90°
  • β = 45°

45

What is the third with 90° and 45°? 45°. Right isosceles.

Example 3

  • α = 30°
  • β = 70°

80

What is the third with 30° and 70°? 80°.

Related calculators

Law of sines calculator

Law of sines (ratio): side a and the angles α and β in degrees.

Use calculator →

Heron formula

Triangle area (Heron): three sides in centimetres.

Use calculator →

All mathematics calculators

Common questions

What is the third angle with 60° and 60°?

60°. 180 − 60 − 60 = 60. Equilateral.

What does the sum of angles in a triangle mean?

In the plane, α + β + γ = 180°. From two angles you compute the rest.

What about 90° and 45°?

45°. Right isosceles. Two acute angles of 45°.

What about 30° and 70°?

80°. 180 − 30 − 70 = 80.

What if the sum exceeds 180°?

The result is a minus. 100° and 90° give −10. The formula does not stop.

Does the order of α and β change the result?

No. 30° and 70° and 70° and 30° both give 80°.

Does this find a side?

No. Angles only. A side lives on the law of sines or cosines.

Do 120° and 30° pass?

Yes. The third is 30°. An obtuse triangle at 120°.

Can the result be larger than 180°?

Yes, if you type minuses. The algebra 180 − α − β does not ask for a drawing.

Does the header currency change the angle?

No. 60 and 60 give 60 under every label.

Knowledge sources

The calculator computes the same formula as the definition below.

Page updated in 2026.