Question 1
1(a):
Line ADB is a straight line.
Find the angle CDB shown below.
ANSWER: Multiple Choice (Type 1)
A: 41\degree
B: 19\degree
C: 71\degree
D: 26\degree
Answer: C
Workings:
Angles on a straight line add up to 180\degree
We have two angles on the straight line, one of which is 109\degree
So the other angle must be 180-109=71\degree
Marks = 2
1(b):
ABCD are points around a circle.
Find the value of x
ANSWER: Simple Text Answer
Answer: 75
Workings:
Angles around a point add up to 360\degree
The existing angles added together gives 100+115+70=285
We can find the missing angle by subtracting this from 360 to get 360-285=75
Marks = 2
Question 2
ACB forms a triangle shown below
ABD is a straight line.
2(a):
Find angle x
ANSWER: Simple Text Answer
Answer: 75
Workings:
Angles on a straight line add up to 180\degree
We can find the missing angle by subtracting the existing angle from 180 to get 180-105=75\degree
Marks = 2
2(b):
Find angle y
ANSWER: Simple Text Answer
Answer: 70
Workings:
Angles in a triangle add up to 180
We can subtract the existing angles from 180 to get 180-35-75=70\degree
Marks = 2
Question 3
ACBD forms a quadrilateral shown below.
3(a):
Find x
ANSWER: Simple Text Answer
Answer: 95
Workings:
Angles in a quadrilateral add up to 360.
We can subtract the quadrilateral’s existing angles from 360 to find the missing angle.
This gives us 360-115-85-65=95\degree.
Marks = 2
3(b):
Find y
ANSWER: Simple Text Answer
Answer: 85
Workings:
Angles on a straight line add up to 180
To find the missing angle subtract the existing angle from 180
This gives us 180-95=85\degree
Marks = 2
Question 4
4(a):
ABC forms an isosceles triangle shown below.
Find x
ANSWER: Simple Text Answer
Answer: 55
Workings:
Angles in a triangle add up to 180
In an isosceles triangle the base angles are identical
We can subtract the given angle from 180 and divide the result by 2 to find the size of each.
180-70=110
x=\dfrac{110}{2}=55\degree
Marks = 2
4(b):
EDF forms an isosceles triangle shown below.
Find the value of y
ANSWER: Simple Text Answer
Answer: 58
Workings:
The base angles of an isosceles triangle are identical, so F must also be 61\degree
All angles in a triangle add up to 180\degree
We can subtract the existing angles from 180 to find E
180-61-61=58\degree
Marks = 2
Question 5
A compound shape is shown in the diagram below.
ADEC forms a quadrilateral
ABC is an isosceles triangle
FAD is a straight line
Angle CAD = x\degree
Angle BAC = y\degree
Angle ABC = z\degree
5(a):
Find x
ANSWER: Simple Text Answer
Answer: 80
Workings:
The angles of a quadrilateral add up to 360
We can subtract the existing angles from 360 to find the missing angle
360-130-85-65=80\degree
Marks = 2
5(b):
Find y
ANSWER: Simple Text Answer
Answer: 76
Workings:
Angles on a straight line add up to 180
We can subtract the given angles from 180 to find the missing angle
180-24-80=76\degree
Marks = 2
5(c):
Find z
ANSWER: Simple Text Answer
Answer: 52
Workings:
The base angles in an isosceles triangle are identical
The angles in a triangle add up to 180
We can subtract the existing angle from 180 and divide the result by 2 to find z
180-76=104
\dfrac{104}{2}=52\degree
Marks = 2