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Interior and Exterior Angles Worksheet

Interior and Exterior Angles Worksheet

Help your students prepare for their Maths GCSE with this free interior and exterior angles worksheet of 30 + questions and answers

  • Section 1 of the interior and exterior angles worksheet contains 20+ skills-based interior and exterior angles questions, in 3 groups to support differentiation
  • Section 2 contains 3 applied interior and exterior angles questions with a mix of worded problems and deeper problem solving questions
  • Section 3 contains 3 foundation and higher level GCSE exam style questions on interior and exterior angles 
  • Answers and a mark scheme for all interior and exterior angles questions are provided
  • Questions follow variation theory with plenty of opportunities for students to work independently at their own level
  • All questions created by fully qualified expert secondary maths teachers
  • Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Interior and exterior angles at a glance

 

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 geometry worksheets, for example a simplifying expressions worksheet or simultaneous equations 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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