How this instrument works
Every triangle's three interior angles always add up to exactly 180°, regardless of the triangle's shape or size — a fixed, universal fact of flat (Euclidean) geometry. Knowing any two of those three angles immediately hands over the third with plain subtraction: 180° minus the two known angles.
This makes finding a missing triangle angle one of the simplest calculations in all of geometry — no trigonometry, no side lengths, and no special triangle type required, just the one universal constraint every triangle obeys.
The two known angles must together stay under 180°, since a third angle of 0° or less would mean the triangle has already collapsed flat or doesn't exist at all.
- Enter the first known angle into the Angle A field.
- Enter the second known angle into the Angle B field.
- Read Angle C: 180° minus the two known angles.
- Add all three angles together and confirm the total comes to exactly 180°.
Worked example — 50° and 60°
A triangle with two known angles, 50° and 60°, has a third angle of 180°−50°−60°=70°. Checking: 50+60+70=180, confirming the universal sum.
A right triangle with one other 45° angle has a third angle of 180°−90°−45°=45° — an isosceles right triangle. Two 60° angles give a third angle of 60° as well — an equilateral triangle, every angle equal.
Questions
Why do a triangle's angles always sum to 180°?
It's a fundamental fact of flat (Euclidean) geometry, true for every triangle regardless of shape or size — one of the earliest theorems proven in classical geometry, and a direct consequence of how parallel lines and straight angles behave on a flat plane.
How do you find a triangle's third angle?
Subtract the two known angles from 180° — no trigonometry or side-length information is needed at all, since the 180° sum alone fully determines the missing angle.
What if the two known angles already sum to 180° or more?
Then no valid triangle exists with those two angles — the third angle would have to be zero or negative, which describes a flattened or impossible shape rather than a genuine triangle.
Does this work for right triangles too?
Yes — a right triangle simply has one of its three angles fixed at 90°, and the same 180°-minus-the-other-two rule finds the remaining angle exactly as it would for any other triangle.
Does the type of triangle (scalene, isosceles, equilateral) change this rule?
No — every triangle, regardless of its side lengths or how its angles compare to each other, always has interior angles summing to exactly 180°.