year 8 maths

628
11 a AB looks like a straight line but the angles do not add to
180°.
b The two angles make a revolution but they do not add to
360°.
c Same as part a.
12 a a + 3b = 360
b a + 2b = 180
c a + b = 90
13 a a = 110
b (a + 50)° should be the larger looking angle.
14 a 30 b 54 c 55
d 34 e 30 f 17
Exercise 6B
1 a equal
b supplementary
c equal
2 a ∠BCH b ∠ABE c ∠GCB d ∠BCH
e ∠FBC f ∠GCB g ∠FBC h ∠DCG
3 a alternate a = b b alternate a = b
c cointerior a + b = 180° d corresponding a = b
e corresponding a = b f cointerior a + b = 180
4 Note: there are other reasons that may be acceptable.
a a = 110 (corresponding angles on parallel lines)
b = 70 (angles on a straight line)
b a = 120 (alternate angles on parallel lines)
b = 60 (angles on a straight line)
c = 120 (corresponding angles on parallel lines)
c a = 74 (alternate angles on parallel lines)
b = 106 (cointerior angles on parallel lines)
c = 106 (vertically opposite angles)
d a = 100 (angles on a straight line)
b = 100 (corresponding angles on parallel lines)
e a = 95 (corresponding angles on parallel lines)
b = 85 (angles on a straight line)
f a = 40 (alternate angles on parallel lines)
b = 140 (angles on a straight line)
5 a a = 58 (cointerior angles on parallel lines)
b = 58 (cointerior angles on parallel lines)
b a = 141 (cointerior angles on parallel lines)
b = 141 (cointerior angles on parallel lines)
c a = 100 (cointerior angles on parallel lines)
b = 80 (cointerior angles on parallel lines)
d a = 62 (cointerior angles on parallel lines)
b = 119 (cointerior angles on parallel lines)
e a = 105 (cointerior angles on parallel lines)
b = 64 (corresponding angles on parallel lines)
f a = 25 (alternate angles on parallel lines)
b = 30 (alternate angles on parallel lines)
6 a No, the alternate angles are not equal.
b Yes, the cointerior angles are supplementary.
c No, the corresponding angles are not equal.
7 a 250 b 320 c 52
d 40 e 31 f 63
g 110 h 145 i 33
8 a 130° b 95° c 90°
d 97° e 65° f 86°
9 a ∠AOB = (180 − a)°
b ∠AOB = (360 − a)°
c ∠AOB = (180 − a − b)°
10 a = 36, b = 276, c = 155, d = 85, e = 130, f = 155, g = 15
Exercise 6C
1 a right-angled triangle b isosceles triangle
c acute-angled triangle d equilateral triangle
e obtuse-angled triangle f equilateral triangle
g isosceles triangle
h scalene triangle
2 a scalene b isosceles c isosceles
d equilateral e scalene f isosceles
3 a right b obtuse c acute
4 a 80 b 40 c 58
d 19 e 34 f 36
5 a 68 b 106 c 20
6 a 65 b 40 c 76
7 a 160 b 150 c 80
d 50 e 140 f 55
8 a yes b no c yes
d yes e yes f yes
9 a 55 b 60 c 25
10 a ∠ACB = 60° (angle in an equilateral triangle)
∠DCE = ∠ACB = 60° (vertically opposite angles)
∴ a = 60
b ∠ACB + 22° + 29° = 180° (angle sum of △ ABC)
∴ ∠ACB = 129°
a = 360 − 129 = 231 (angles in a revolution)
c △ ABC is isosceles (AB = AC)
∠BCA = ∠ABC = 72° (equal angles are opposite equal
sides in △ ABC)
a + 90 + 72 = 180 (angle sum of △ ABC)
a = 18
d ∠CAB = 25° (angles on a straight line)
∠ACB = 64° (angles on a straight line)
a + 25 + 64 = 180 (angle sum of △ ABC)
a = 91
e ∠CAB = ∠CBA = a° (equal angles are opposite
equal sides)
∠ACB = ∠DCE = 49° (vertically opposite angles)
a + a + 49 = 180 (angle sum of △ ABC)
2a = 131
a = 65.5
f ∠ACB = 30° (angles on a straight line)
a + 90 + 30 = 180 (angle sum of △ ABC)
a = 60
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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