Angles Explained
8 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
An angle measures the turn between two lines that meet at a point. We usually measure it in degrees, where a full turn is 360°. Angles are the language of geometry, and a handful of relationships let you find unknown angles without measuring.
Types of angle
| Type | Size |
|---|---|
| Acute | Less than 90° |
| Right | Exactly 90° |
| Obtuse | Between 90° and 180° |
| Straight | Exactly 180° |
| Reflex | Between 180° and 360° |
Angle pairs
- Complementary: add to 90°. The complement of 35° is 55°.
- Supplementary: add to 180°. The supplement of 110° is 70°.
- Vertical (opposite) angles: formed when two lines cross, and always equal.
- Angles around a point add to 360°.
Parallel lines and a transversal
When a line crosses two parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior angles add to 180°. These let you carry an angle from one line to another.
Angles in triangles
The angles of a triangle add up to 180°. If two are 50° and 60°, the third is 70°. The exterior angle at a vertex equals the sum of the two opposite interior angles: 50° + 60° = 110°, which is 180° − 70°.
Angles in polygons
The interior angles of an n-sided polygon add up to (n − 2) × 180°. A hexagon: 4 × 180° = 720°, so each angle of a regular hexagon is 120°. A regular octagon: 6 × 180° = 1,080°, so each is 135°. Practise on the geometry quiz.
Degrees and radians
Mathematicians often measure angles in radians, where 180° = π. See degrees vs radians.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Solve a triangle with sides 5, 12 and 13.
Show answer
Side a: 5 · Side b: 12 · Side c: 13
- Find sin, cos and tan of 45°.
Show answer
sin: 0.7071067812 · cos: 0.7071067812 · tan: 1
- Area of a circle with radius 7.
Show answer
Area: 153.93804
Frequently asked questions
What is a reflex angle?
An angle greater than 180° and less than 360°.
Are vertical angles always equal?
Yes.
How do I find the angle sum of a polygon?
Use (n − 2) × 180°, where n is the number of sides.
What is a transversal?
A line that crosses two or more other lines.
Try it yourself
Triangle CalculatorSolve any triangle from three sides, two sides and an angle, or two angles and a side.Trigonometry CalculatorFind sin, cos, tan, csc, sec and cot of any angle, or the inverse trig functions.Geometry CalculatorArea, perimeter, circumference, volume and surface area of common shapes.Keep learning
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