What This Calculator Does
The Interior Angles of a Triangle Calculator finds the missing third angle of any triangle when you already know the other two. Geometry tells us that the three interior angles of every triangle always add up to exactly 180 degrees. Using that rule, this tool instantly works out the remaining angle and confirms whether the triangle you've described is actually possible.
The Inputs You Provide
There are just two fields to fill in:
- First Angle (degrees): one of your known interior angles.
- Second Angle (degrees): a second known interior angle.
Both values should be entered in degrees. The calculator does the rest — no need to enter the third angle, since that's exactly what it computes for you.
The Formula
The calculation is based on the angle sum property of triangles:
Third Angle = 180° − Angle₁ − Angle₂
After finding the third angle, the tool also checks that the triangle is valid. A triangle is valid only when all three angles are greater than zero and the first two angles together add up to less than 180°. It also reports the total sum of all three angles, which should always equal 180° for a correct result.
Worked Example
Suppose you enter a First Angle of 60° and a Second Angle of 80°.
- Third Angle = 180 − 60 − 80 = 40°
- Sum = 60 + 80 + 40 = 180°
- Valid? All angles are positive and 60 + 80 = 140 is less than 180, so the triangle is valid.
If instead you entered 120° and 70°, the third angle would calculate as 180 − 120 − 70 = −10°. Because that result is negative, the calculator flags the triangle as invalid — no such triangle exists.
Frequently Asked Questions
Why do the angles always add up to 180°?
This is a fundamental theorem of Euclidean geometry. Any flat (planar) triangle's interior angles sum to 180 degrees, regardless of its shape or size.
What does "invalid" mean here?
It means your two entered angles are impossible for a real triangle — either one is zero or negative, or the two together already meet or exceed 180°, leaving no room for a positive third angle.
Can I use this for right or equilateral triangles?
Yes. For a right triangle, enter 90° and one other angle. For an equilateral triangle, enter 60° and 60° to confirm the third angle is also 60°.
