year 8 maths

352 Chapter 6 Angle relationships and properties of geometrical figures 1
Key ideas
■ When two straight lines meet they form two pairs of vertically opposite angles . Vertically
opposite angles are equal.
w°
v°
t°
u°
t = v
u = w
■ If one of the four angles in vertically opposite angles is a right angle, then all four angles are
right angles.
B
C
z° x°
y°
D
A
x = 90
y = 90
z = 90
• AB and CD are perpendicular lines . This is written as AB ⟂ CD .
A
■ The markings in these diagrams indicate that:
• AB = AD
• BC = CD
• ∠ABC = ∠ADC
D
C
B
Example 1
Finding the value of pronumerals in geometrical figures
Determine the value of the pronumeral in these diagrams, giving reasons.
a
b° b
a°
30°
65°
a°
b°
SOLUTION
a a + 30 = 90 (angles in a right angle)
a = 60
b + 90 = 360 (angles in a revolution)
b = 270
b a + 65 = 180 (angles on a straight line)
a = 115
b = 65 (vertically opposite angles)
EXPLANATION
a° and 30° are adjacent complementary angles.
b° and 90° make a revolution.
a° and 65° are adjacent supplementary angles.
b° and 65° are vertically opposite angles.
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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