Angles & Geometry

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

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)