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Test on Angles
1
In the following figure, ABCD is a rectangle, CDE is an isosceles triangle and EFGC is a
parallelogram.
E
F
D
C
A
G
B
Without using a protractor, determine the measure of each of the 3 following angles and justify one of
your answers.
m DEC
m FGC
m BCG
2
Given the following figure :
c a d
50
b
Without using geometry instruments, find the measure of angles a and b and justify each of your
answers.
3
In a triangle in which AB  BC and angle B measures 50, what is the measure of angle A?
4
Given rectangle ABCD below.
B
C
30
E
?
A
D
Each diagonal of this rectangle measures 12 cm and the measure of angle CBE is 30.
What is the measure of angle AED?
Justify each step of your work by stating the appropriate geometric reason.
5
Which is the right angle in this diagram?
T
S
E
R
0
6
Many directions are shown on the face of a compass. Use the figure below to answer the question
which follows.
N-N-W
N
N-N-E
N-W
N-E
W-N-W
E-N-E
W
E
W-S-W
E-S-E
S-W
S-E
S-S-W
S
S-S-E
Find the measures of the angles between the following directions :
a) N and N-W
b) S and S-W
c) N-E and S-E
d) S-W and SS-E
7
What is the sum of the measures of the acute angles within this dodecagon?
8
Wayne has just spent his first day at hockey school. With the help of a protractor, measure his
shooting angles.
a)
b)
c)
d)
e)
9
Find the measures of the angles indicated on the figure below with the help of a protractor.
B
C
A
D
10
What is the measure of each angle in the following triangle?
3
2
1
11
The figure shown is a rectangle with both diagonals.
2
1
3
5
6
Which statement below is FALSE?
A)
Angles 1 and 2 are complementary.
B)
Angles 1 and 3 are congruent.
C)
Angles 5 and 6 are adjacent.
D)
Angles 5 and 6 are supplementary.
4
12
In which figure are angles 1 and 2 congruent because they are vertically opposite angles?
Shade in the letter of the answer chosen.
13
A)
C)
B)
D)
In the figure on the right, lines AE and CF intersect
at point B. Line segment BE is the bisector of
angle DBF and angle CBD measures 50.
E
D
50
B
C
A
What is the measure of angle ABF?
A)
65
C)
115
B)
100
D)
130
F
14
A
Given the following figure.
65
65
D
C
B
Which two statements below allow you to conclude that angle ACD measures 130?
15
A)
In any isosceles triangle, the angles opposite the congruent sides are congruent.
Vertical angles are congruent.
B)
The sum of the measures of the interior angles of a triangle is 180.
Two adjacent angles whose exterior sides are parallel are supplementary.
C)
The sum of the measures of the interior angles of a triangle is 180.
Vertical angles are congruent.
D)
In any isosceles triangle, the angles opposite the congruent sides are congruent.
Two adjacent angles whose exterior sides are parallel are supplementary.
In the following figure, ray FC is the
bisector of angle DCE.
E
F
?
52°
B
C
What is the measure of angle BCE?
A)
52
C)
64
B)
60
D)
76
D
16
Triangle ABC to the right is isosceles.
Sides AB and BC are congruent.
The measure of angle B is 40.
B
40
What is the measure of angle A?
A
17
A)
40
C)
90
B)
70
D)
140
C
Triangle ABC is right-angled at B.
A
130
B
C
Which of the following statements is true?
A)
The measure of angle A is 40.
C)
The measure of angle A is 50.
B)
The measure of angle A is 45.
D)
The measure of angle A is 55.
18
In the diagram below, AB and CD are perpendicular.
DF is the bisector of angle CDE. The measure of angle BDE is 18.
C
F
E
18o
A
D
B
What is the measure of angle CDF?
19
A)
72
C)
45
B)
54
D)
36
Angle A in rhombus ABCD is 80.
Given this fact, which of the following
deductions is correct?
A)
B)
C)
D)
D  A and is 80.
D  B and is 200.
D  B and is 100.
D  C and is 100.
B
A
C
80
D
20
In the figure on the right, ABCD is a rectangle.
Angle AOD measures 50. Line segment OF is the
bisector of angle COD and the height of
triangle COD.
A
B
50
D
O
F
C
Match each statement on the left with the appropriate reason that can be used to calculate the degree
measure of angle FCO.
Statement
1.
2.
3.
4.
21
Reason
m AOB = 180  m AOD
m AOB = 180  50 = 130
A)
The sum of the measures of the interior
angles of a triangle is 180.
B)
In any right triangle, the acute angles
are complementary.
C)
Adjacent angles whose external sides
are in a straight line are supplementary.
D)
The bisector of an angle divides it into
two congruent angles.
E)
The angles opposite a vertex are
congruent.
m DOC = m AOB = 130
m DOF = m FOC =
130
= 65
2
m FCO = 180  (m OFC + m FOC)
m FCO = 180  (90 + 65) = 25
Five streets all meet at the same point.
Racine Street forms a right angle with Bégin Street. Léger Street forms an acute angle with Racine
Street and an obtuse angle with Bégin Street. Roy Street forms an obtuse angle with Léger Street.
Laurier forms a right angle with Léger Street.
Draw a sketch of the intersection showing the names of the streets.
22
Here is a map of the cross country ski trail called "The Mouse".
The mouse
START
A
3 km
B
1
2
C
3
F
G
E
D
Measure the angles identified by the numbers 1, 2 and 3. Your answer must be accurate to the nearest
degree.
Identify the type or category of each of the angles. (acute, obtuse, straight, right or reflex)
23
It's summer and you are windsurfing. Your sail is in the shape of a right-angled isosceles triangle.
Find the measure of the 3 angles of the sail.
24
Based on the information given on the figures below, calculate the measure of each angle named.
Note: Figures are not drawn to scale.
a)
B
?
110
A
C
D
b)
m ADB =

m G =

m L =

m RST =

E
85
?
30
F
G
c)
K
J
d)
?
20
L
Q
P
R
?
S
35
T
25
In the figure on the right, m AE  m BE .
Angle BEC is 60.
Angles PAC and RAB are straight angles.
P
A
B
R
60
E
What is the measure of angle RAP?
Give a reason (in words) for each step or
calculation.
D
C