Angles & Geometry
Angle types, triangle properties, quadrilaterals and symmetry
Explanation
Types of Angles
- Acute: less than 90°
- Right: exactly 90°
- Obtuse: between 90° and 180°
- Straight: exactly 180°
- Reflex: between 180° and 360°
Angle Relationships
| Rule | Meaning |
|---|---|
| Complementary angles | Sum to 90° |
| Supplementary angles | Sum to 180° |
| Angles at a point | Sum to 360° |
| Vertically opposite | Equal (formed by crossing lines) |
| Corresponding angles | Equal (parallel lines, same side) |
| Alternate angles | Equal (parallel lines, opposite sides) |
| Co-interior angles | Sum to 180° (parallel lines, same side) |
Triangles
Angles in any triangle sum to 180°.
- Equilateral: all sides and angles equal (60° each)
- Isosceles: two equal sides and two equal base angles
- Scalene: no equal sides or angles
- Right-angled: one 90° angle
Quadrilaterals & Polygons
Angles in any quadrilateral sum to 360°.
Key shapes: square, rectangle, rhombus, parallelogram, trapezium, kite
Interior Angles of Polygons
Sum of interior angles = (n − 2) × 180° where n = number of sides
Example: Pentagon (5 sides): (5−2) × 180 = 540°
Each angle in a regular pentagon = 540° ÷ 5 = 108°
Pythagoras & Key Tips
In a right-angled triangle: a² + b² = c² where c is the hypotenuse (longest side).
Example: Find the hypotenuse if the other sides are 3 and 4.
c² = 3² + 4² = 9 + 16 = 25 → c = 5
Key Tips
- Always give a reason for each angle found in geometry proofs
- Mark equal angles and sides on your diagram as you work
- Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17)
Practice Questions
Test your knowledge of Angles & Geometry with a timed quiz. Answers are revealed at the end.
Take Quiz →