Triangle Sum Theorem Calculator

Triangle Angle Sum Theorem

The interior angles of any triangle always add to $180°$ (or $\pi$ radians):

$$\alpha + \beta + \gamma = 180°$$

Given two angles, solve for the third:

$$\gamma = 180° - \alpha - \beta$$

If $\alpha = 52°$ and $\beta = 68°$, then $\gamma = 180° - 120° = 60°$. The triangle is acute because all angles are less than $90°$.

What is the third angle if two angles are 40° and 75°?

180° − 40° − 75° = 65°.

Can a triangle have two 90° angles?

No. Two right angles would sum to 180°, leaving 0° for the third angle, which is impossible.

Do triangle angles always sum to 180°?

Yes, in Euclidean geometry. This is the triangle angle sum theorem.

What if two angles are 60° each?

The third angle is also 60°, forming an equilateral triangle.