Education

Triangle Missing Angle Calculator

Enter two interior angles of a triangle and leave the third blank. The calculator finds the missing angle, checks the 180° total, and classifies the triangle by angles.

triangle-missing-angle
Missing angle
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Angle set—
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How the missing triangle angle is found

Every triangle has interior angles that add to 180°. If you know two angles, the missing angle is the amount needed to reach 180°. OpenStax covers this in its lesson on properties of angles, triangles, and the Pythagorean theorem.

This calculator is useful for ordinary triangle angle problems, but it also gives the angle classification. That helps students answer follow-up questions like whether the triangle is acute, right, or obtuse.

Formula

A + B + C = 180° Missing angle = 180° - known angle 1 - known angle 2

The formula works for every triangle: scalene, isosceles, equilateral, acute, right, or obtuse. The side lengths may change the shape, but the interior angle sum remains 180° in standard Euclidean geometry.

Worked example

Angle A = 40° Angle B = 65° Angle C = 180° - 40° - 65° Angle C = 75° The angles are 40°, 65°, and 75°. All are less than 90°, so the triangle is acute.

Common mistakes

A missing angle cannot be 0° or negative. If the two known angles already add to 180° or more, they cannot form a triangle. Another common mistake is using 360°, which belongs to a full turn or some quadrilaterals, not the interior angles of a triangle.

Common questions

  • Add the two known angles and subtract that total from 180 degrees. For example, if the known angles are 50° and 60°, the missing angle is 180° - 110° = 70°. This works because the three interior angles of every triangle add to 180°.
  • No. A right angle is 90°. Two right angles would already add to 180°, leaving no space for the third angle. A triangle can have exactly one right angle, and the other two angles must be acute angles that add to 90°.
  • A negative missing angle means the given angles cannot form a triangle. For example, 100° and 90° already add to 190°, which is more than the total angle sum of a triangle. In that case, the issue is not the calculator; the input values are impossible for a triangle.
  • If one angle is exactly 90°, the triangle is right. If one angle is greater than 90°, it is obtuse. If all three angles are less than 90°, it is acute. The calculator uses the completed angle set to classify the triangle after the missing value is found.
  • Yes, but isosceles triangles have an extra property: two angles are equal when the two opposite sides are equal. If you know an isosceles triangle has a vertex angle of 40°, the two base angles share the remaining 140°, so each base angle is 70°.
  • In Euclidean geometry, the interior angles of a triangle form a straight angle when rearranged, and a straight angle measures 180°. This is one of the first geometry facts students use to solve missing-angle problems, prove triangle properties, and work with polygons.