Angles in squares and polygons.
Answer the questions about the internal angles of various polygons.

🙂 = Correct, ☹️ = Incorrect

📌 Rules

• Interior angles of any quadrilateral add up to 360°: Squares and rectangles have four 90° right angles (4 × 90° = 360°). For any four-sided shape, subtract the three known angles from 360° to find the missing angle.

• Calculate the total interior angle sum for any polygon: Split the shape into triangles from one vertex, or use the formula (n – 2) × 180°, where n is the number of sides:

– Pentagon (5 sides):(5 – 2) × 180° = 3 × 180° = 540°

– Hexagon (6 sides):(6 – 2) × 180° = 4 × 180° = 720°

– Octagon (8 sides):(8 – 2) × 180° = 6 × 180° = 1080°

• Find individual interior angles in regular polygons: Since all angles in a regular polygon are equal, divide the total angle sum by the number of sides (e.g. regular pentagon: 540° ÷ 5 = 108°; regular hexagon: 720° ÷ 6 = 120°).

💡 Tips

• Memorise key total angle sums:

– Triangle (3 sides):180°

– Quadrilateral (4 sides):360°

– Pentagon (5 sides):540°

– Hexagon (6 sides):720°

– Octagon (8 sides):1080°

• Quick typing on our platform: Typing your answer is designed to be super quick and simple! Just type plain numbers like 360, 108, or 120 without adding the degree symbol (°), letters, or spaces.

⚠️ Warnings

• Do not confuse regular and irregular polygons: You can only divide the total angle sum equally among angles if the shape is regular (all sides and angles equal).

• Do not rely on measuring with a protractor: Diagrams are often not drawn to scale! Always use polygon angle rules to calculate missing values.