Every polygon's interior angles add up to a fixed total that depends only on its number of sides — no measuring required, just one formula.
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When a line crosses two parallel lines, it creates several equal pairs of angles — three named relationships, all from one picture.
📊 Angle pairs
| Angle pair | Rule |
|---|---|
| Complementary | Two angles that add up to 90° |
| Supplementary | Two angles that add up to 180° |
| Corresponding angles (parallel lines) | Equal — in the same position at each crossing |
| Alternate angles (parallel lines) | Equal — on opposite sides of the transversal |
| Co-interior / allied angles | Add up to 180° — on the same side, between the lines |
Worked example: the complement of 35° is 90−35=55°. The supplement of 110° is 180−110=70°.
A triangle always obeys two fixed rules about its angles, no matter its shape or size.
📌 The two triangle angle rules
Angle sum property: the three interior angles of any triangle always add up to 180°.
Exterior angle theorem: an exterior angle equals the SUM of the two remote (non-adjacent) interior angles.
Worked example: if two interior angles are 50° and 60°, the exterior angle at the third vertex is 50+60=110°.
The sum of a polygon's interior angles depends only on how many sides it has — one formula covers every polygon.
🏆 Polygon interior angle sum = (n−2) × 180°
| Polygon | Sides (n) | Interior angle sum |
|---|---|---|
| Pentagon | 5 | (5−2)×180 = 540° |
| Hexagon | 6 | (6−2)×180 = 720° |
| Octagon | 8 | (8−2)×180 = 1080° |
For a REGULAR polygon (all sides and angles equal), divide the sum by the number of sides to find one interior angle. A regular hexagon: 720÷6=120° per angle. The sum of EXTERIOR angles of any polygon is always 360°.
12 questions on angles, parallel lines, triangles and polygons.
