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Maths Quest 9 for New South Wales 5.3 pathway
Chapter 3 Geometry Test B
Geometry Test B
1
Name: ___________________________
Section A Multiple Choice
1
The value of the pronumeral x is:
A
B
C
D
2
3
A
4
The value of the pronumeral y is:
100°
90°
80°
20°
A quadrilateral with only opposite sides B
equal in length is called a:
A square
B rectangle
C kite
D rhombus
The value of the pronumeral x is:
A
B
C
D
5
20°
30°
50°
60°
45°
95°
110°
205°
The value of the pronumeral m is:
C
D
A
B
C
D
A
B
C
D
A
6
70°
90°
110°
125°
The value of the pronumeral t is:
A
B
C
D
83°
97°
103°
277°
A
Maths Quest 9 for New South Wales 5.3 pathway
Chapter 3 Geometry Test B
7
The value of the angle which is
complementary to 27° is:
A
72°
B
63°
C
153°
D
163°
B
8
The value of the angle, a, in the figure
below is:
B
11
The value of x in the figure shown is:
A
B
C
D
A
B
C
D
9
10
111°
69°
79°
89°
The size of each of the interior angles of A
a regular pentagon is:
A
108°
B
180°
C
540°
D
900°
The value of the angle, a, in the figure
below is:
A
B
C
D
28°
62°
118°
59°
D
2
B
48
54
102
126
12
Has how many star polygons does a
regular hexagon have?
A 1
B 2
C 3
D 8
A
13
In which one of the following shapes do A
the diagonals always form four
congruent triangles?
A Square
B Rectangle
C Trapezium
D Parallelogram.
Maths Quest 9 for New South Wales 5.3 pathway
14
In the diagram, if a  b  160 , then x
equals:
A
B
C
D
70
110
200
290
Chapter 3 Geometry Test B
A
15
The corresponding angle to c is:
A
B
C
D
a
f
g
h
3
C
Maths Quest 9 for New South Wales 5.3 pathway
Chapter 3 Geometry Test B
Geometry Test B
4
Name: ___________________________
Section B Short/Extended answer
1
Find the value of the pronumeral (answer to
nearest whole degree).
(a)
(b)
(c)
6
(a ) x  3 x  90  180
4 x  90  180
4 x  90
x  22.5
x  23 (to the nearest degree)
(b) x  1  2 x  1  50  180
3 x  50  180
3 x  130
x  43.3
x  43 (to the nearest
degree)
(c) 4 x  3  3 x  2  2 x  180
9 x  1  180
9 x  181
x  20.1
x  20 (to the nearest
degree)
Maths Quest 9 for New South Wales 5.3 pathway
2
Chapter 3 Geometry Test B
Find the value of the pronumeral/s in each of
the following.
(a)
(b)
5
6
(a) y  80
(b) 3x  85  8 x
5 x  85
x  17 
(c)
3
Find the value of the pronumeral in each of the
following to the nearest degree.
(a)
(c) 4 x  x  30
3 x  30
x  10
y  180  10  30
y  140
6
(a) 3x  3x  2 x  2 x  360
10 x  360
x  36
(b)
(c)
(b) x  1  x  5  54  90  360
2 x  150  360
2 x  210
x  105
(c) 5 x  x  4 x  7  3 x  2  360
13 x  5  360
13 x  355
x  27.3
x  27 (to the nearest
degree)
Maths Quest 9 for New South Wales 5.3 pathway
4
Chapter 3 Geometry Test B
(a)
A polygon has 8 sides. Find the sum of its (a)
angles.
(b)
A regular polygon has 10 sides. Find the
size of each of its angles.
(b)
6
180  (82)
= 180  6
= 1080°
4
180  (102)
= 180  8
= 1440°
Each angle = 1440 ÷ 10
Each angle = 144
5
Find the value of the pronumeral.
(a)
4
(a)
180  (5  2)  540
x  140  140  100  100  540
x  480  540
x  60 0
(b)
(b)
180  (6  2)  720
y  y  105  105  125  125  720
2 y  460  720
2 y  260
y  130 0
4
6
Indicate two pairs of :
(a) co-interior angles
(b) corresponding angles.
Possible solutions
y w, v x
(a)
s y , x r , v p, w q
(b)
Maths Quest 9 for New South Wales 5.3 pathway
7
8
9
Chapter 3 Geometry Test B
Find the value of the pronumerals, giving
reasons.
Two transversal lines cross a pair of parallel
lines at 154° and 136°. Find the angle, x,
between the transversals.
Use a ruler and a protractor to construct
triangles that have:
(a) one side of length 3 cm and another of
5 cm with an angle of 70° between them
(b)
angles of 80° and 35° with the side
between them of length 4 cm.
7
2
x = 39 (corresponding angles are equal)
y = 39 (vertically opposite angles are equal)
z = 51 (complementary angles add up to 90)
wx = 141 (co-interior angles are
supplementary)
x  26  44  180
x  70  180
3
x  110
4
(a)
(b)
Maths Quest 9 for New South Wales 5.3 pathway
10
Chapter 3 Geometry Test B
Determine the values of the angles a, b, c and d 32 + 82 + a = 180 (supplementary)
in the figure below, giving reasons.
114 + a = 180
a = 66°
8
3
b = 82° (vertically opposite)
c = 66° (vertically opposite to a)
d = 32° (vertically opposite)
11
Determine the values of the angles a, b and c in a + 109 = 180 (supplementary)
the figure below, giving reasons.
+ 109 a = 71°
3
b = 71° (alternate)
c = 71 (corresponding to a or vertically
opposite to b)
12
Determine the sum of each of the exterior
angles in a regular nonagon (a nine-sided
figure).
Sum of angles = 360°
Each angle = 360° ÷ 9
Each angle = 40°
2
13
Construct a triangle PQR, with base
PQ = 8 cm, side PR = 6 cm and angle
PQR = 40°.
(1)
(2)
4
List the steps in your construction
(3)
(4)
Draw a base of 8 cm.
With compass at one end of the base,
construct an arc (PR) of 6 cm.
With a protractor at the other end of the
base draw a line of 40° (PQR).
Join the point where the arc and line PR
meet to the point Q.
Maths Quest 9 for New South Wales 5.3 pathway
14
Find the value of x.
Chapter 3 Geometry Test B
(3x  1)  x  73  180
3x 1  x  73  180
4x  72  180
4x  108
x  27
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