Angles in Triangles

In a Nutshell

The three interior angles of any triangle always add up to 180°180°.

No matter the shape of a triangle — equilateral, isosceles, scalene, right-angled — the sum of its three interior angles is always 180°180°.

You can prove this by tearing off the three corners of any paper triangle and placing them together: they always form a straight line (180°180°).

To find a missing angle in a triangle, add the two known angles and subtract from 180°180°:

missing angle=180°(angle 1+angle 2)\text{missing angle} = 180° - (\text{angle 1} + \text{angle 2})

Triangle angle sum explorer An interactive triangle where you can adjust two angles and see that all three always sum to 180 degrees.
Angle A: Angle B:

Adjust angles A and B with the buttons. Angle C updates automatically so that the three always sum to 180°180°.

Watch it work

Question: A triangle has angles of 52°52° and 76°76°. Find the third angle.

Have a go

Q1. A triangle has angles 60°60° and 60°60°. Find the third angle.

Q2. A right-angled triangle has one angle of 34°34°. Find the third angle.

Q3. An isosceles triangle has a top angle of 40°40°. Find the two equal base angles.

Q4. Can a triangle have two obtuse angles? Explain.