Trigonometry

Angle Calculator

Find missing angles in triangles and calculate interior angles of regular polygons. Essential for GCSE and A-Level geometry and trigonometry questions.

Angle A (°)

Angle B (°)

Missing angle

45°

How it works

Angles in a triangle sum to 180°
$a + b + c = 180°$
The three interior angles of any triangle always add up to 180°.
Find the missing angle
$c = 180° - 60° - 75° = 45°$
c = 180 − 60 − 75 = 45°.
Result:45°

Angles in a Triangle

a + b + c = 180°

a, b, c

The three interior angles of the triangle

Example substitution

c = 180° - 60° - 75° = 45°

If two angles are 60° and 75°, the missing angle is 45°.

Worked examples

A triangle has angles of 55° and 72°. Find the missing angle.

1
Angles in a triangle sum to 180°: a + b + c = 180°
2
Substitute known angles: 55° + 72° + c = 180°
3
Solve for c: c = 180° − 55° − 72° = 53°

Answer: Missing angle = 53°

Find the interior angles of a regular hexagon (6 sides).

1
Sum of interior angles formula: (n − 2) × 180°
2
Substitute n = 6: (6 − 2) × 180° = 4 × 180° = 720°
3
Each angle (regular polygon): 720° ÷ 6 = 120°

Answer: Each interior angle = 120°, total = 720°

Find the sum of interior angles of a pentagon (5 sides).

1
Use the formula: (n − 2) × 180°
2
Substitute n = 5: (5 − 2) × 180° = 3 × 180°
3
Calculate total: 3 × 180° = 540°

Answer: Sum of interior angles = 540°

Frequently asked questions

What do angles in a triangle add up to?+

Angles in a triangle always add up to 180°.

What is the sum of interior angles in a polygon?+

Sum = (n − 2) × 180°, where n is the number of sides.

What do angles on a straight line add up to?+

180°.

What do angles at a point add up to?+

360°.

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