What Is the Third Angle Calculator?
This calculator finds the missing third angle of a triangle when you already know the other two angles. It relies on one of the most fundamental rules of geometry: the interior angles of any triangle always add up to 180 degrees. This is true for every triangle — equilateral, isosceles, scalene, right, acute, or obtuse — making the tool universally applicable.
How to Use It
Enter the measures of any two known angles, A and B, in degrees. Click calculate and the tool returns angle C, the third angle. If the result is zero or negative, the two angles you entered are too large to form a valid triangle (their sum already reaches or exceeds 180°).
The Formula Explained
The governing equation is $$C = 180^{\circ} - A - B$$ Because \(A + B + C = 180^{\circ}\), rearranging for \(C\) gives 180° minus the sum of the two known angles. There is no need for trigonometry here — it is pure angle arithmetic.
Worked Example
Suppose a triangle has angles A = 60° and B = 70°. Then $$C = 180^{\circ} - 60^{\circ} - 70^{\circ} = 50^{\circ}.$$ Checking: \(60 + 70 + 50 = 180^{\circ}\), confirming a valid triangle.
FAQ
Does this work for right triangles? Yes. If one angle is 90°, simply enter it as A or B and the calculator returns the remaining angle.
What if my answer is negative? A negative or zero result means the two angles entered cannot belong to the same triangle, since their sum must be less than 180°.
Can I use radians? This tool uses degrees. To convert, multiply radians by \(180/\pi\) before entering values.
