year 8 maths

366 Chapter 6 Angle relationships and properties of geometrical figures 1
Example 4
Using the exterior angle theorem
Find the value of a .
C
A
a°
161°
B
SOLUTION
a + 90 = 161 (exterior angle of △ ABC )
a = 71
Alternatively:
∠ ABC + 161 = 180 (angles on a straight line)
∠ ABC = 19
a + 19 + 90 = 180 (angle sum of a triangle)
a = 71
EXPLANATION
Use the exterior angle theorem for a triangle.
The exterior angle ( 161° ) is equal to the sum
of the two opposite interior angles.
Alternatively, find ∠ ABC (19°) , then use the
triangle angle sum to find the value of a .
Exercise 6C
UNDERSTANDING AND FLUENCY
1–6, 7(½) 2, 3, 4(½), 5–6, 7(½) 4(½), 5–6, 7(½)
1 Give the common name of a triangle with these properties.
a one right angle b two equal side lengths
c all angles acute d all angles 60°
e one obtuse angle f three equal side lengths
g two equal angles
h three different side lengths
2 Classify these triangles as scalene, isosceles or equilateral.
a b c
d e f
3 Classify these triangles as acute, right or obtuse.
a b c
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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