Angles in Polygons: Fluency and Exam Drill - Worksheets, Questions and Revision

23 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Geometry and Measures

4.11D Angles in Polygons: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
State, in degrees, the sum of the interior angles of a triangle.
(Total for Question 1 is 1 mark)
2
A polygon has 13 sides.
Calculate the sum of its interior angles.
(Total for Question 2 is 2 marks)
3
A polygon has 11 sides.
Calculate the sum of its interior angles.
(Total for Question 3 is 2 marks)
4
A polygon has 14 sides.
Calculate the sum of its interior angles.
(Total for Question 4 is 2 marks)
5
A regular polygon has 45 sides.
Work out the size of each interior angle.
(Total for Question 5 is 2 marks)
6
A regular polygon has 30 sides.
Work out the size of each exterior angle.
(Total for Question 6 is 2 marks)
7
The exterior angle of a regular polygon is 9 degrees.
Work out the number of sides of the polygon.
(Total for Question 7 is 2 marks)
8
The interior angle of a regular polygon is 170 degrees.
Work out the number of sides of the polygon.
(Total for Question 8 is 3 marks)
9
The interior angle of a regular polygon is 174 degrees.
Work out the number of sides of the polygon.
(Total for Question 9 is 3 marks)
10
In a quadrilateral, three of the angles measure 97 degrees, 112 degrees and 94 degrees.
Work out the size of the fourth angle.
(Total for Question 10 is 2 marks)
11
In a pentagon, four of the angles measure 118 degrees, 96 degrees, 102 degrees and 89 degrees.
Work out the size of the fifth angle.
(Total for Question 11 is 2 marks)
12
A regular polygon has 72 sides.
Work out the size of each exterior angle.
(Total for Question 12 is 2 marks)
13
A polygon has 16 sides.
Calculate the sum of its interior angles.
(Total for Question 13 is 2 marks)
14
A polygon has 100 sides.
State the sum of its exterior angles.
(Total for Question 14 is 1 mark)
15
For a certain regular polygon, the sum of its interior angles is 10 times the sum of its exterior angles.
Work out the number of sides of the polygon.
(Total for Question 15 is 3 marks)
16
Nadia says: 'A regular polygon can have an interior angle of exactly 173 degrees.'
Show, using calculations, that Nadia is wrong.
(Total for Question 16 is 3 marks)
17
In a pentagon, three of the angles measure 101 degrees, 109 degrees and 113 degrees. The remaining two angles are in the ratio 3 : 4.
(a)Form and solve an equation to find the value of one part of the ratio.(3)
(b)Hence work out the size of the larger of the two remaining angles.(1)
(Total for Question 17 is 4 marks)
18
An irregular pentagon has exterior angles of 58 degrees, 71 degrees, 91 degrees, 63 degrees and y degrees.
(a)Work out the value of y.(2)
(b)Work out the size of the interior angle at the vertex where the exterior angle is y degrees.(1)
(Total for Question 18 is 3 marks)
19
The six exterior angles of a hexagon, in degrees, are x, x + 4, x + 8, x + 12, x + 16 and x + 20.
(a)Show that 6x + 60 = 360.(1)
(b)Solve the equation to find the value of x.(2)
(c)Work out the size of the largest interior angle of the hexagon.(2)
(Total for Question 19 is 5 marks)
20
A dart-shaped (concave) quadrilateral has three interior angles of 43 degrees, 51 degrees and 38 degrees, and a reflex interior angle at the fourth vertex.
Work out the size of the reflex angle, explaining how you know it is reflex.
(Total for Question 20 is 3 marks)
21
A polygon gains 3 extra sides (no vertex becomes a straight line).
By how much does the sum of its interior angles increase?
(Total for Question 21 is 2 marks)
22
Priya is designing a tiled floor using two regular octagons and one square meeting at every vertex, with no gaps or overlaps.
Show, using calculations, that this arrangement fits exactly around a point.
(Total for Question 22 is 3 marks)
23
Let sum(n) = (n - 2) * 180 be the sum of the interior angles of a polygon with n sides.
(a)Prove algebraically that sum(n + 1) - sum(n) = 180 for every whole number n, showing that increasing the number of sides of a polygon by 1 always increases the sum of its interior angles by exactly 180 degrees.(3)
(b)A polygon with 22 sides has an interior angle sum of 3600 degrees. Using the result from part (a), write down the sum of the interior angles of a polygon with 23 sides.(2)
(Total for Question 23 is 5 marks)
Mark scheme · 4.11D Angles in Polygons: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23