Cambridge Essentials Mathematics Support 9 GM1.2 Answers
GM1.2
Answers
1 a
b
c
d
e
f
g
h
i
2 Shapes b order 3, d order 4, e order 2, f order 5, h order 6, i order 2
3 a Regular shapes b, d, f, h
b a isosceles triangle, b equilateral triangle, c scalene triangle, d square, e rectangle
f regular pentagon, g irregular pentagon, h regular hexagon, i irregular hexagon
c For regular shapes:
number of lines of symmetry = order of rotational symmetry = number of sides
Original Material © Cambridge University Press 2010
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Cambridge Essentials Mathematics Support 9 GM1.2 Answers
4 a 8
b 8
5 a 360° ÷ 5
b 2 sides are radii and so the same length
c (180° – 72°) ÷ 2 = 54°
d 10 lots of angle y make up the angles in a pentagon
e Check students’ drawings of an inscribed regular pentagon within a circle of radius 4 cm.
6 a 360° ÷ 6
b (180° – 60°) ÷ 2 = 60°
c equilateral triangle
d sum of angles in a hexagon = 12  y = 12  60 = 720°
e Check students’ drawings of an inscribed regular hexagon within a circle of radius 4 cm.
7 a 360° ÷ 8 = 45°
b (180° – 45°) ÷ 2 = 67.5°
c 67.5°  2  8 = 1080°
d Check students’ drawings of an inscribed regular octagon within a circle of radius 4 cm.
8 a 360° ÷ 10 = 36°
b Check students’ drawings of an inscribed regular decagon within a circle of radius 4 cm.
9 a 360° ÷ 12 = 30°
b Check students’ drawings of an inscribed regular dodecagon within a circle of radius 4 cm.
10 a 360° ÷ 5 = 72°
b 180° – 72° = 108°
Original Material © Cambridge University Press 2010
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Cambridge Essentials Mathematics Support 9 GM1.2 Answers
c 108°  5 = 540°
11 a 360° ÷ 8 = 45°
b 180° – 45° = 135°
c 135°  8 = 1080°
12 a To find each exterior angle, divide 360 by the number of exterior angles or sides:
exterior angle =
360
number of exterior angles or sides
b To find each interior angle, subtract the size of an exterior angle from 180:
interior angle = 180 – size of an exterior angle
c To find the angle sum, multiply the size of one interior angle by the number of interior angles
or the number of sides:
angle sum = size of an interior angle  number of interior angles or sides
13
Regular polygon
Exterior
angle
120°
Interior
angle
60°
Angle sum
Equilateral triangle
Number of
sides
3
Square
4
90°
90°
360°
Pentagon
5
72°
108°
540°
Hexagon
6
60°
120°
720°
Octagon
8
45°
135°
1080°
Decagon
10
36°
144°
1440°
Dodecagon
12
30°
150°
1800°
Icosagon
20
18°
162°
3240°
Original Material © Cambridge University Press 2010
180°
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Cambridge Essentials Mathematics Support 9 GM1.2 Answers
*14a 10°
b 36
c 36
d 36  170 = 6120 i.e. interior angle multiplied by number of interior angles or sides (36)
*15a 20°
b 18
c 18
d 18  160 = 2880 i.e. interior angle multiplied by number of interior angles or sides (18)
16 a 145°
b 135°
17 a 110°
b 110°
*18a In a pentagon there are 3 triangles: 3 lots of 180° which give 540°.
b In a hexagon there are 4 triangles: 4 lots of 180° which give 720°.
c The number of triangles is 2 less than the number of sides of the polygon.
d angle sum = (number of sides – 2)  180°
angle sum for a decagon = (12 – 2)  180° = 1800°
Original Material © Cambridge University Press 2010
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