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Angles & Polygons

NotesQuestionsFlashcards

Types of Angles

Acute: less than 90°. Right angle: exactly 90°. Obtuse: between 90° and 180°. Reflex: between 180° and 360°.

Angle Rules

Angles on a straight line sum to 180°. Angles at a point sum to 360°. Vertically opposite angles are equal. Angles in a triangle sum to 180°. Angles in a quadrilateral sum to 360°.

Polygons

The sum of interior angles of an n-sided polygon = (n − 2) × 180°. Each interior angle of a regular polygon = (n − 2) × 180° / n. Interior + exterior angle = 180°. Sum of exterior angles = 360° for any polygon.

Sum of interior angles = (n − 2) × 180°

Key Points

  • Angles on a straight line = 180°
  • Angles at a point = 360°
  • Interior angles of polygon = (n-2) × 180°
  • Exterior angles of any polygon sum to 360°

Exam Tips

  • Always state the angle rule you are using (e.g., "angles on a straight line")
  • For polygon questions, identify n (number of sides) first
  • Show your working even for simple angle calculations