Angles
The angles in a triangle always add up to 180°, and in a polygon the sum depends on the number of corners. Try it yourself.
The explanation is shown. Quick: the answer. Advanced: the exterior angles of the triangle — or a table of polygons from 3 to 12 corners.
Your numbers
Answer
Angle C
70°
The triangle is acute.
How to work it out
- 1A + B + C = 180°
- 2C = 180° − 50° − 60° = 70°
The formula
A + B + C = 180°
The angles in a triangle always add up to 180°.
(n − 2) · 180°
The angle sum of a polygon with n corners — it can be split into n − 2 triangles.
360° / n
The exterior angle of a regular polygon.
In depth: more numbers and “what if”
The triangle's angles
| Angle | Size | Exterior angle | Kind |
|---|---|---|---|
| A | 50° | 130° | acute angle |
| B | 60° | 120° | acute angle |
| C | 70° | 110° | acute angle |
More: Geometry
- PythagorasFind the missing side, set out a right angle, check whether a room is square, and find the space diagonal.
- Area and perimeterRectangle, triangle, trapezium, circle and composite shapes — area and perimeter.
- Volume and surface areaBox, cylinder, cone, sphere, pyramid, prism, pipe and frustum — also in litres.
- The circleRadius, circumference and area from one measurement — plus sector, annulus, chord and rise.
- Right triangleSine, cosine and tangent: all sides and angles from two known values.
- Points in the coordinate systemDistance, midpoint and the line between two points — drawn in.
- Similar figuresScale factor and missing sides — area is multiplied by k², volume by k³.
- Any triangleThe sine and cosine rules: find the rest from SSS, SAS, ASA or SSA.
- TransformationsReflect, rotate and translate a figure on a coordinate grid — before and after.