IGCSE/GCSE Mathematics - Polygon Angles

When it comes to IGCSE/GCSE Maths, do you remember how to calculate the sum of interior angles?

• All the interior angles of a triangle add up to 180°. 

• If we have 2 triangles making up this shape, the sum (total) of the interior angles = 2 x 180 = 360°.
• The same trick applies to other polygons, for example:

• Here the sum of the interior angles = 3 x 180 = 540°.
• The Sum of a Polygon's interior angles = The number of sides minus 2 multiplied by 180.
• Using the shorthand letter n to represent the number of sides we get the formula:

Sum of interior angles = (n - 2) x 180.

• If you have a regular polygon (pentagon, hexagon etc.) all the interior angles will be the same, so to find one interior angle you just divide the sum of the interior angles by the number of sides.

• The interior angles are shown in red and the exterior angles are shown in blue.
• The interior angle of a polygon and the exterior angle both add up to 180°.
• The sum of all the exterior angles of any polygon = 360°.

That's the end of the topic!

CLICK HERE TO LEARN MORE ABOUT OUR IGCSE/GCSE MATHEMATICS COURSES

Drafted by Bonnie (Mathematics)