Angles-In-Polygons Edexcel Foundation

Angles in polygons

What is a polygon?

• A polygon is a 2D shape with straight sides

  • A triangle is a polygon with 3 sides

  • A quadrilateral polygon with 4 sides

  • A pentagon is a polygon with 5 sides

• In a regular polygon all the sides are the same length and all the angles are the same size

  • A regular polygon with 3 sides is an equilateral triangle

  • A regular polygon with 4 sides is a square

What are the interior angles and the exterior angles of a polygon?

• Interior angles are the angles inside a polygon at the corners

• The exterior angle at a corner is the angle needed to make a straight line with the interior angles

  • It is not the angle that forms a full turn at the corner

• The interior angle and exterior angle add up to 180° at each corner

What is the sum of the interior angles in a polygon?

• To find the sum of the interior angles in a polygon of sides, use the rule

  • Sum of interior angles =

    • This formula comes from the fact that -sided polygons can be split into triangles

• Remember the sums for these polygons

  • The interior angles of a triangle add up to 180°

  • The interior angles of a quadrilateral add up to 360°

  • The interior angles of a pentagon add up to 540°

What is the sum of the exterior angles in a polygon?

• The exterior angles in any polygon always sum to 360°

How do I find the size of an interior or exterior angle in a regular polygon?

• To find the size of an interior angle in a regular polygon:

• Method 1
  Find the sum of the interior angles

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