Download Geometry review

STRAND: Space
TOPIC:
Polygons & polyhedra
Geometry review
Definitions
Complementary angles are angles whose sum is 90°.
Supplementary angles are angles whose sum is 180°.
Concurrent lines are lines which pass through the one point, forming angles which sum up to 360°.
A triangle is a plane, three sided figure. The angle sum is 180° (supplementary).
A quadrilateral is a plane, four sided figure. The angle sum is 360°.
WORKED Example 1
WORKED Example 2
2x + 20°
x 40°
x + 5°
x
40°
3x 3x
2x
2x
3x + 21°
Find the value of x.
Find the value of x. State whether the angles in this
diagram are complementary or supplementary.
Solution
Solution
The angles formed at the point where the
concurrent lines meet sum to 360°.
40° + (x + 5°) + x + 3x + 3x + 40° + 2x + x = 360°
(Add the angles)
11x + 85 = 360
(Simplify the left side)
11x = 275
(Subtract 85 from both sides)
x = 25°
(Divide both sides by 11)
The diagram above shows that the three angles sum to
90° so they are complementary angles.
(2x + 20°) + 2x + (3x + 21°) = 90° (Add the angles)
7x + 41 = 90
(Simplify the left side)
41 + 7x = 49
(Subtract 41 from both sides)
41 + x = 7°
(Divide both sides by 7)
Try these.
1 State whether each of the following sets of angles are complementary, supplementary or neither.
a 47°, 43°
b 123°, 57°
c 15°, 40°, 3°, 32°
d 104°, 11°, 75°
e 39°, 31°, 110°
f 26°, 14°, 150°
g 67°, 90°, 13°
h 33°, 55°, 82°
i 9°, 50°, 42°
j 34°, 10°, 54°, 2°
k 7°, 170°, 3°
l 109°, 1°, 77°, 3°
2 Find the value of x in each of the following.
a
b
3x
5x
3x + 10°
2x + 40°
 John Wiley & Sons Australia, Ltd 2001
STRAND: Space
TOPIC:
Polygons & polyhedra
SKILLBUILDER: Geometry review
3 Find the value of each pronumeral in the following diagrams.
a
b
c
5x + 4°
4x + 15°
a
3x
67° c
6x + 3°
5x + 25°
b
3x + 20°
3x
33°
d
e
f
x
75°
y
x
2y
68°
4y
g
h
i
a
105°
4x
120°
88°
a
c
z
d b
c e
b
5y + 30°
j
4x + 12°
k
l
3x
5x + 22°
5x + 24°
5x + 24°
2y 2y + 14°
2y + 20°
108°
3x + 10°
 John Wiley & Sons Australia, Ltd 2001