GCSE Maths · Higher · Chapter 6: Angles · Lesson 1

Angle facts, triangles and parallel lines

Grades 4–6About 45 minutesNo calculator35 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
An isosceles triangle has a top angle of $11 8^{\circ}$ . Find one base angle.
[1 mark]
Answer
A2
From chapter 4
Find the next term: $5, 15, 45, 135, \dots$
[1 mark]
Answer
A3
Last lesson
After a $20%$ increase a price is £96. Find the original price.
[1 mark]
Answer
A4
Key Stage 3
Reflect $(- 1, 4)$ in the $x$ -axis.
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

The two lines are parallel. Work out the value of $x$ , and the size of each angle.

Not drawn accurately

Hint Corresponding angles are equal, so set the two expressions equal.

B1
The two lines are parallel. Work out the value of $x$ , and the size of each angle.
[3 marks]
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Answer $x = \dots\dots$ angle $= \dots \dots^{\circ}$

Grades 4–5

C1
Four angles meet at a point. Work out the value of $x$ .
[2 marks]
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Answer
C2
A straight line crosses two parallel lines. Work out the size of angle $y$ . Give a reason for your answer.
[2 marks]
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Answer

C3
The angles of a triangle are in the ratio $2 : 3 : 7$ . Work out the size of the largest angle.
[2 marks]
Answer
C4
An isosceles triangle has one angle of $11 2^{\circ}$ . Work out the size of each of its other two angles.
[2 marks]
Answer
C5
Two straight lines cross. Work out the value of $x$ , and then the size of angle $y$ .
[3 marks]
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Answer $x = \dots\dots$ $y = \dots \dots^{\circ}$
C6
In triangle $A B C$ the side $B C$ is extended to $D$ . Work out the value of $x$ .
[2 marks]
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Answer

Grades 5–6

D1
Amir says, "A triangle can have angles of $x^{\circ}$ , $(x + 60)^{\circ}$ and $(x + 150)^{\circ}$ ."
Explain why Amir is wrong.
[2 marks]

D2
$L A$ is parallel to $B C D$ . In triangle $A B C$ , $A B = A C$ . Angle $L A B = 6 4^{\circ}$ .
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(a)
Work out angle $A B C$ . Give a reason for your answer.
[2 marks]
Answer
(b)
Work out angle $A C B$ . Give a reason for your answer.
[2 marks]
Answer
(c)
Work out angle $B A C$ and angle $A C D$ .
[2 marks]
Answer $B A C = \dots \dots^{\circ}$ $A C D = \dots \dots^{\circ}$
Total for D2: 6 marks
D3
$P QR$ is an isosceles triangle with $P Q = P R$ . The side $QR$ is extended to $S$ . Angle $QP R = 2 x^{\circ}$ and angle $P R S = (5 x - 10)^{\circ}$ . Work out the size of angle $QP R$ . You must show your working.
[4 marks]
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Answer

Grade 7 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use angle facts for lines, points and triangles.
I can use vertically opposite angles and the exterior angle of a triangle.
I can find angles at parallel lines and give the reason.

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