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Angles in Polygons | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What is a polygon?

  • A polygon is a flat shape with n straight sides.
    • For example, a triangle has 3 sides, a quadrilateral has 4 sides, and a pentagon has 5 sides.
  • In a regular polygon, all sides are of equal length and all angles are equal.
    • For example, an equilateral triangle is a regular polygon with 3 sides, and a square is a regular polygon with 4 sides.

Question for Angles in Polygons
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How many sides does a regular hexagon have?
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What are the sums of angles in polygons?

  • To work with angles in polygons, you need to calculate the sums of their angles.
  • Use the formula to find the sum of the interior angles in a polygon with n sides:
    • SUM OF INTERIOR ANGLES = 180° × (n – 2)
    • This is because the polygon can be divided into (n – 2) triangles.
  • For regular polygons, divide this sum by n to find each individual interior angle.
  • The sum of the exterior angles of any polygon always equals 360°.
    • TOTAL OF EXTERIOR ANGLES = 360°
  • Exterior angles are the angles formed by extending each side of the polygon along a straight line.
  • Note that the interior and exterior angles at each vertex lie on a straight line, summing to 180°.

Angles in Polygons | Mathematics for GCSE/IGCSE - Year 11

The document Angles in Polygons | Mathematics for GCSE/IGCSE - Year 11 is a part of the Year 11 Course Mathematics for GCSE/IGCSE.
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FAQs on Angles in Polygons - Mathematics for GCSE/IGCSE - Year 11

1. What is a polygon?
Ans. A polygon is a closed two-dimensional shape with straight sides. It is formed by connecting line segments called edges, which meet at points called vertices.
2. What are the sums of angles in polygons?
Ans. The sum of interior angles in a polygon can be calculated using the formula (n-2) * 180 degrees, where n represents the number of sides of the polygon.
3. How can I calculate the measure of each interior angle in a regular polygon?
Ans. To find the measure of each interior angle in a regular polygon, divide the sum of interior angles by the number of sides in the polygon. This will give you the measure of each interior angle.
4. Are there any special properties of angles in certain types of polygons?
Ans. Yes, regular polygons have all angles and sides congruent, while in irregular polygons, angles and sides can vary in size and length.
5. How can I determine the type of polygon based on its interior angles?
Ans. By calculating the sum of interior angles in a polygon and comparing it to the known formulas for different types of polygons, you can determine the type of polygon based on its angles.
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