Angle calculator — missing triangle angle, complements and polygon sums

How to use the angle calculator

1. In Find, choose one of: third angle of a triangle, complementary angle, supplementary angle, explementary angle, or interior angle sum of a polygon.
2. For a triangle, enter Angle 1 and Angle 2. For the complement, supplement or explement, enter Angle 1 only.
3. For a polygon, enter the Number of sides (a whole number, 3 or more).
4. Read the result. Angle answers also appear In radians, and the working line shows the subtraction or formula.

What it does and when to use it

Many geometry questions come down to “the angles must add up to a fixed total”. The angles in a triangle make 180°, angles on a straight line make 180°, angles around a point make 360°, and the angles in a right-angle corner make 90°. This tool does that subtraction for you and catches impossible inputs. The polygon mode helps with tiling patterns, woodwork joints such as picture frames and hexagonal planters, and exam questions on interior and exterior angles.

For a full triangle with sides as well as angles, use the triangle solver. The regular polygon calculator adds area, apothem and diagonals. To change units, the angle converter handles degrees, radians and more.

How it works

• Third angle of a triangle: 180° − (angle 1 + angle 2)
• Complementary: 90° − angle
• Supplementary: 180° − angle
• Explementary: 360° − angle
• Polygon: sum = (n − 2) × 180°; each interior angle of a regular polygon = sum ÷ n; each exterior angle = 360° ÷ n

Radians are found by multiplying degrees by π/180. The polygon rule comes from splitting the shape into n − 2 triangles from one corner, each worth 180°.

Worked examples

Third angle, step by step. A triangle has angles of 35° and 85°.

1. Add the known angles: 35 + 85 = 120.
2. Subtract from the triangle total: 180 − 120 = 60.

The working line reads 180° − 120° = 60°, and the tool adds 1.047197551 rad.

Angles on a straight line. One angle is 112°, so its partner is Result: 68°.

Octagon. With 8 sides the sum is (8 − 2) × 180° = 1,080°. For a regular octagon the tool shows Each interior angle (regular): 135° and an exterior angle of 45°. That is why a stop sign’s corners are 135°.

An impossible case. Asking for the complement of 95° returns a warning: “The known angle is 95°, more than the 90° total, so no other angle is possible.”

Limits and tips

• All angle inputs must be greater than zero.
• The calculator does not find angles from side lengths; use the triangle solver for that.
• The polygon mode needs a whole number of sides. A “2.5-sided polygon” returns a message, not a result.
• The calculation runs on your device.