Help your students prepare for their Maths GCSE with this free interior and exterior angles worksheet of 30 + questions and answers
An interior angle of a polygon is an angle on the inside of a vertex of the polygon. The interior angles of a regular polygon are all equal, as are the side lengths. For irregular polygons, the size of each interior angle varies. The sum of the interior angles of any polygon is given by 180(n-2) where n is the number of sides the polygon has. For a regular polygon, the size of one interior angle is found by dividing the total angle sum by the number of angles. For example, a regular hexagon has 6 sides and 6 angles. The angle sum is 180*(6-2)=720° and each interior angle is 720 divided by 6 = 120°.
An exterior angle is the angle formed between the outer edge of a polygon and a straight line extended from the next side. The sum of the exterior angles of any polygon is 360°. To find the size of each exterior angle of a regular polygon we divide 360 by the number of sides the polygon has. For example, the size of one exterior angle of a regular pentagon is 360 divided by 5 = 72°.
Since interior and exterior angles lie on a straight line, they add up to 180°.
Looking forward, students can then progress to additional angles in polygons worksheets and other geometry worksheets, for example an angles in polygons worksheet or area of a triangle worksheet.
For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts
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