What this calculator does
How many degrees in a triangle is one of the fixed facts of plane geometry: the three interior angles of any triangle, no matter its shape or size, always add up to exactly 180°. It holds for a razor-thin sliver of a triangle and for one close to equilateral alike, as long as it is drawn on a flat surface rather than a curved one.
Because the total is fixed, knowing any two of a triangle's three angles is enough to find the third by subtraction. Enter the two known angles below and the calculator returns the missing one, along with what type of triangle that makes.
The formula
The third angle equals 180° minus the sum of the two known angles. Whether that result makes the triangle acute, right-angled or obtuse depends on whether the largest of the three angles is under, exactly, or over 90°.
| Term | Meaning |
|---|---|
| Angle sum | The fixed total of a triangle's three interior angles: always 180°. |
| Acute triangle | Every angle is under 90°. |
| Right-angled triangle | One angle is exactly 90°. |
| Obtuse triangle | One angle is over 90°. |
The inputs explained
| Field | What to enter |
|---|---|
| Known angle 1 (°) | The first known angle, in degrees. |
| Known angle 2 (°) | The second known angle, in degrees. The two must add to less than 180° for a valid triangle. |
When to use it
Finishing a geometry problem
A worksheet or exam question often gives two angles of a triangle and asks for the third; this calculator returns it directly, along with the sum check that shows the working adds to 180°.
Checking a diagram is drawn correctly
If three marked angles on a sketch do not add to 180°, at least one of them is wrong, which is a quick sanity check before relying on the diagram further.
Classifying a triangle from its angles
Once the third angle is known, the triangle can be labelled acute, right-angled or obtuse, and checked for two equal angles, without measuring any side lengths.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
The third angle as the first known angle changes
A second angle held at 60°, with the first angle varying across a range of values.
| First known angle | Third angle | Triangle type by angle |
|---|---|---|
| 20° | 100.00° | Obtuse |
| 40° | 80.00° | Acute |
| 60° | 60.00° | Acute |
| 80° | 40.00° | Acute |
| 100° | 20.00° | Obtuse |
| 119° | 1.00° | Obtuse |
Which combinations of angles give a right or equilateral triangle
A first angle held at 60°, with the second angle varying, showing when the result is right-angled or has repeated angles.
| Second known angle | Third angle | Has two equal angles (isosceles)? | Triangle type by angle |
|---|---|---|---|
| 40° | 80.00° | No | Acute |
| 50° | 70.00° | No | Acute |
| 60° | 60.00° | Yes | Acute |
| 70° | 50.00° | No | Acute |
| 80° | 40.00° | No | Acute |
| 90° | 30.00° | No | Right-angled |
Questions
Why do the angles of a triangle always add up to 180°?
It follows from the parallel postulate of Euclidean geometry: drawing a line through one vertex parallel to the opposite side creates angles that match the triangle's own angles, and those three angles together form a straight line, which is 180° by definition.
Does this still hold for a right-angled or obtuse triangle?
Yes. The 180° total is the same for every flat triangle regardless of its type; only how that total is split between the three angles changes.
Is the 180° rule true for triangles on a sphere or curved surface?
No. On a curved surface, such as the surface of the Earth, a triangle's angles can add up to more than 180°. This calculator, like the 180° rule itself, applies to triangles drawn on a flat plane.
Can I use this if I only know one angle?
No, one angle alone is not enough: infinitely many triangles share a single given angle, with the other two able to take many different combinations that still sum to 180°. Two known angles are needed to pin down the third.
For a full triangle worked from its three side lengths instead of its angles, see the triangle calculator. For a triangle defined by two equal sides and a base, see the isosceles triangle calculator.