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Unit 2 | 19 Angles and quadrilaterals | Student Book chapter 16
19 Angles and quadrilaterals
Angles in quadrilaterals
D
Work out the value of x in each of these quadrilaterals.
D
a
b A
x
C
x
152°
46°
A
38°
73°
B
B
a 46 1 38 1 152 5 236°
Always write
down all the
numbers you
are adding or
subtracting.
You get method
marks for this.
D
35°
C
First add the three angles given.
x 5 360 2 236 5 124°
The angles in a quadrilateral add up to 360°.
b Angle BCD 5 180 2 35 5 145°
The angles on a straight line add up to 180°.
145 1 73 1 90 5 308
Note that the angle on the left is 90°.
x 5 360 2 308 5 52°
The angles in a quadrilateral add up to 360°.
Angles and parallel lines
Write down the value of a, b, c and d.
Give reasons for your answers.
a
d
137°
29°
b
c
a 5 137°
You can see that the angle is more than 90°.
Vertically opposite angles are equal.
Use the words
alternate and
corresponding,
NOT Z and F.
Learn this reason.
b 5 137°
Again you can see that the angle is more than 90°.
Alternate angles are equal.
You can think of alternate angles as angles in a Z.
c 5 180° 2 137° 5 43°
It is best to show your working.
Angles on a straight line add up to 180°
d 5 29°
Corresponding angles
are equal.
Learn the wording for this reason.
You can see the angle is less than 90°.
You can think of corresponding angles as angles in an F.
If you are not sure then it is worth noting that the angles more than 90° are likely to be the same, the
angles less than 90° are likely to be the same and the obtuse and acute angles are likely to add up to 180°.
Unit 2 | 19 Angles and quadrilaterals | Student Book chapter 16
Now try these
1
Questions on this spread are targeted at the grades indicated.
Work out the missing angles below:
a
117°
a
b
D
c
b
88°
71°
134°
53°
79°
d
128°
c
55°
84°
e
130°
67°
f
e
41°
f
152°
d
2
55
71°
92°
98°
In the diagrams below, work out the size of each of the angles marked with a letter.
Give a reason for each of your answers for a to g.
47°
a
d
52°
b
116°
e
f
c
i
135°
g
h
44°
j
38°
l
k
m
No.19
ABCD is a straight line.
PQ is parallel to RS.
i Write down the size of the angle marked y.
ii Give a reason for your answer.
(2 marks)
A
x
P
(March 2008)
Again, knowing what corresponding and alternate angles are gets you easy
marks here. y is an alternate angle to the angle marked 50° so your 2 marks
are for saying that angle y 5 50° and giving the reason that they are
alternate angles.
B
50°
C
R
y
Q
S
Diagram NOT
accurately drawn
D
No.14
James says, ‘The lines AB and DC are parallel.’
Ben says, ‘The lines AB and DC are not parallel.’
Who is right, James or Ben?
Give a reason for your answer.
(2 marks)
A
D
Diagram NOT
accurately drawn
(June 2009)
96°
88°
Many students knew that Ben was correct, the lines are
B
C
not parallel, but unless they gave some idea of why they
thought this, they got no marks. The answer is that if the lines were parallel the two angles would add up to 180°.
Write down the sum of these two angles (88 1 96 5 184) to show that you have worked this out.