Angles and Shape: Practice Set 3
Angles and Shape: Practice Set 3 moves into interior angle sums for polygons with more than four sides, using the rule that the interior angles of any polygon add up to (n - 2) x 180 degrees, alongside further practice on parallel line angle facts and multi-step angle problems that combine several rules in one question. It follows the two earlier Angles and Shape sets.
Before you start
Make sure you're comfortable with these topics first:
Method
- To find the sum of the interior angles of any polygon, use the rule (n - 2) x 180 degrees, where n is the number of sides.
- To find one interior angle of a regular polygon, divide the total interior angle sum by the number of sides, since all interior angles in a regular polygon are equal.
- Remember that the exterior and interior angle at any vertex lie on a straight line and so add up to 180 degrees, which lets you switch between the two if you know one.
- When several angle facts apply to the same diagram, work through them one at a time, writing down each new angle you find before using it in the next step.
- For algebraic angle questions, set up an equation using the relevant angle sum rule, then solve it using the standard steps for solving equations.
- Always check whether the question wants an interior angle, an exterior angle, or the number of sides, since these are easy to confuse under time pressure.
Worked example
A regular polygon has an exterior angle of 24 degrees. (a) Calculate the number of sides of the polygon. (b) Calculate the size of one interior angle.
- Exterior angles of any polygon add up to 360 degrees, so the number of sides is 360 / 24.
- 360 / 24 = 15, so the polygon has 15 sides. This is the answer to part (a).
- The interior angle and the exterior angle at each vertex lie on a straight line, so the interior angle is 180 - 24.
- 180 - 24 = 156 degrees. This is the answer to part (b).
Practice questions
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Q1Calculate the sum of the interior angles of a hexagon (6 sides).Show answer
Answer: 720 degrees ((6 - 2) x 180)
Q2A regular pentagon has 5 equal sides and 5 equal angles. Calculate the size of one interior angle.Show answer
Answer: 108 degrees (540 / 5, since the interior angle sum of a pentagon is (5 - 2) x 180 = 540)
Q3A polygon has an interior angle sum of 1080 degrees. Calculate the number of sides.Show answer
Answer: 8 sides (1080 / 180 = 6, so n - 2 = 6 and n = 8)
Q4A regular polygon has an exterior angle of 40 degrees. Calculate the number of sides.Show answer
Answer: 9 sides (360 / 40)
Q5A quadrilateral has angles of 80 degrees, 95 degrees, x degrees and x degrees. Find x.Show answer
Answer: 92.5 degrees (80 + 95 + 2x = 360, so 2x = 185)
Q6An irregular pentagon has angles of 100, 110, 120, 130 and y degrees. Find y.Show answer
Answer: 80 degrees (540 - 100 - 110 - 120 - 130)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A regular polygon has 9 sides. (a) Calculate the sum of its interior angles. (b) Calculate the size of one interior angle.
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A regular polygon has an interior angle of 165 degrees. (a) Calculate the size of one exterior angle. (b) Calculate the number of sides of the polygon. (c) Calculate the sum of all the interior angles of this polygon.
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In a quadrilateral, the four angles are in the ratio 2:3:4:6. (a) Write an expression for each angle in terms of x, where the angles are 2x, 3x, 4x and 6x. (b) Form and solve an equation to find x. (c) State the size of the largest angle, and identify whether it is acute, obtuse or reflex.
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Free printable worksheet
Want more practice on paper? Download the angles and shape: practice set 3 worksheet pack - 20 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 27 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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