Targeting Grade C

1
GCSE Mathematics
Targeting Grade C
Shape and Space Unit 4 Interior/Exterior
Angles
2
TOP Interior Angle Sum Practice 1
Regular Polygons TAIL 1 Practice 2 All
polygons TAIL 2

• Can you
• Methods to calculate the
• interior/exterior angles of any polygon
• Work out angles in regular polygons
• Try a test
• Calculate angles in polygons
• Try
  a test

If not you need
3
TOP
Remember There are 2 ways of doing this
Method 1
To find the Interior Angle Sum (IAS) for an n
sided polygon
x exterior angle y interior angle
The exterior angles of any polygon sum to 360
Each Exterior Angle x 360 n
So For a regular hexagon Each exterior angle
360 6 60 Each interior angle 180 - 60
120
Each Interior Angle y 180 - x
Next
4
TOP
Remember There are 2 ways of doing this
Method 2
To find the Interior Angle Sum (IAS) for an n
sided polygon
Any polygon can be split into (n-2) triangles
The IAS is the sum of all the triangles180(n-2)
Each Interior Angle IAS n
So For a regular pentagon IAS 180(5-2) 180
x 3 540 Each interior angle 540 5 108
Each Exterior Angle 180 - Interior angle
Lesson
5
Are you ready for the answers ?
Practice 1 Regular Ploygons
1.
A decagon is a polygon with 10 sides. Work out
the size of each exterior angle of a regular
decagon
360 10 36
2.
The size of each exterior angle of a regular
polygon is 40. Work out the number of sides of
the polygon
360 40 9 sides
3.
Diagram NOT accurately drawn Work out the size of
each interior angle of a regular octagon.
360 8 45 180 45 135
4.
The size of each exterior angle of an regular
polygon is 24. Work out the number of sides the
polygon has.
360 24 15 sides
Lesson
6
Are you ready for the answers ?
TAIL 1
1.
The size of each exterior angle of a regular
polygon is 30. Work out the number of sides of
the polygon.
360 30 12 sides
2.

• Work out the size of an exterior angle of a
  regular pentagon. (2)
• The area of the pentagon is 8560 mm2.
• Change 8560 mm2 to cm2. (2)
• Each side of another regular pentagon has a
  length of 101 mm, correct to the nearest
  millimetre.
• (c) (i) Write down the least possible length of
  each side.
• (ii) Write down the greatest possible length
  of each side. (2)
• (Total 6 marks)

a) 360 5 72
b) 8560 (10 x 10) 85.6
c) (i) 100.5
(ii) 101.5
Lesson
7
Are you ready for the answers ?
Practice 2
1.
The diagram shows a 5 sided shape. All of the
sides of the shape are equal in length.

• (i) 60
• (ii)) Top triangle is equilateral

(a) (i) Find the value of x. (ii) Give a reason
for your answer. (b) Work out the value of y.

(Total 4 marks)
(b) 90 60 150
Next
8
Are you ready for the answers ?
Practice 2
2.

• 60
• 360 90 90 60 120
• 6 x 2 12cm²

This is part of the design of a pattern found at
the theatre of Diana at Alexandria. It is made
up of a regular hexagon, squares and equilateral
triangles. (a) Write down the size of the angle
marked x. (1) (b) Work out the size of
the angle marked y. (2) The area of each
equilateral triangle is 2 cm2. (c)
Work out the area of the regular
hexagon. (2) (Total 5 marks)
Lesson
9
Are you ready for the answers ?

TAIL 2
1.
The diagram shows a shape. The shape is a
6-sided polygon. (a) Write down the mathematical
name for a 6-sided polygon.
(1 mark)
Hexagon
The diagram below shows how the shape tessellates.
The size of each of the angles marked x is
135. (b) Give reasons why.
(2 marks)
360 90 270 270 2 135 Angles at a point
add up to 360
Next
10
TAIL 2
Are you ready for the answers ?
1. contd
The diagram shows the lengths of two of the sides
of the shape. (c) Work out the perimeter of the
shape.
(2 marks) (Total 5 marks)
P (30 x 4) (8 x 2) 136 cm
Lesson