Sec 1 Maths Angles and parallel lines worksheet with answers

A free Sec 1 Maths worksheet on angles and parallel lines: 9 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 Maths worksheet: Angles and parallel lines

Total: 30 marksSuggested time: 45 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

In the diagram, the straight lines

AB

and

CD

meet at

O

. Find

x

Answer[1]

\angle ABC

and

\angle PQR

are supplementary angles. Find

x

Answer[2]

In the diagram,

AB

is parallel to

CD

. The reflex angle

BED

(3x + 15)^\circ

. Find

x

Answer[3]

In the diagram,

AB

is parallel to

CD

. Which side of triangle

PQS

is the longest? Choose the answer.

Answer[3]

Section B

(a)In the diagram,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer (a)[2]

(b)In the diagram, the line segments

OA

OB

OC

and

OD

meet at the point

O

. Find

x

Answer (b)[2]

(a)In the diagram,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer (a)[2]

(b)In the diagram, the line segments

OA

OB

and

OC

meet at the point

O

. Find

x

Answer (b)[2]

(a)In the diagram, the line segments

OA

OB

OC

and

OD

meet at the point

O

. Find

x

Answer (a)[2]

(b)In the diagram,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer (b)[2]

(a)In the diagram,

AB

is parallel to

CD

. Find

x

Answer (a)[2]

(b)In the diagram, the straight lines

AB

and

CD

meet at

O

OE

is a straight line between

OA

and

OC

. Find

x

Answer (b)[2]

(a)In the diagram, the straight lines

AB

and

CD

meet at

O

. Find

x

Answer (a)[1]

(b)In the diagram,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer (b)[1]

(c)In the diagram,

AB

is parallel to

CD

. Find

x

Answer (c)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

x = 122

(vert. opp. ∠s)[1]

x = 122

(vert. opp. ∠s)

Question 2

Answer:

x = 97

(supplementary ∠s)[2]

x^\circ + 83^\circ = 180^\circ

x = 180 - 83

x = 97

(supplementary ∠s)

Question 3

Answer:

x = 93

[3]

Draw the line

EF

through

E

, parallel to

AB

and

CD

, pointing towards

B

and

D

. It splits the angle

BED

inside the bend into

\angle BEF

and

\angle FED

\angle BEF = 38^\circ

(alt. ∠s,

AB \parallel EF

)

\angle FED = 28^\circ

(alt. ∠s,

CD \parallel EF

)

(3x + 15)^\circ + 38^\circ + 28^\circ = 360^\circ

(∠s at a pt.)

3x + 81 = 360

3x = 279

x = 93

Question 4

Answer: PS[3]

\angle PQS = \angle APQ

\phantom{\angle PQS} = 79^\circ

(alt. ∠s,

AB \parallel CD

)

\angle PSQ = \angle BPS

\phantom{\angle PSQ} = 34^\circ

(alt. ∠s,

AB \parallel CD

)

\angle QPS = 180^\circ - 79^\circ - 34^\circ

\phantom{\angle QPS} = 67^\circ

(∠s on a str. line)The largest angle is

79^\circ

, at

Q

, so the longest side is

PS

, opposite it.

Question 5

(a)Answer:

x = 71

[2]

x^\circ + 109^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 109

x = 71

(b)Answer:

x = 168

(∠s at a pt.)[2]

48^\circ + 90^\circ + 54^\circ + x^\circ = 360^\circ

x = 360 - 48 - 90 - 54

x = 168

(∠s at a pt.)

Question 6

(a)Answer:

x = 62

[2]

x^\circ + 118^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 118

x = 62

(b)Answer:

x = 96

(∠s at a pt.)[2]

129^\circ + x^\circ + 135^\circ = 360^\circ

x = 360 - 129 - 135

x = 96

(∠s at a pt.)

Question 7

(a)Answer:

x = 107

(∠s at a pt.)[2]

57^\circ + 101^\circ + 95^\circ + x^\circ = 360^\circ

x = 360 - 57 - 101 - 95

x = 107

(∠s at a pt.)

(b)Answer:

x = 35

[2]

3x - 25 = 2x + 10

(corr. ∠s,

AB \parallel CD

)

3x - 2x = 10 + 25

x = 35

Question 8

(a)Answer:

x = 113

[2]

Draw the line

EF

through

E

, parallel to

AB

and

CD

, pointing away from

A

and

C

. It splits

x^\circ

into

\angle BEF

and

\angle FED

\angle BEF = 47^\circ

(alt. ∠s,

AB \parallel EF

)

\angle FED = 66^\circ

(alt. ∠s,

CD \parallel EF

)

x = 47 + 66

x = 113

(b)Answer:

x = 64

(vert. opp. ∠s)[2]

\angle AOC = 28^\circ + 36^\circ

\angle AOC = 64^\circ

x = 64

(vert. opp. ∠s)

Question 9

(a)Answer:

x = 122

(vert. opp. ∠s)[1]

x = 122

(vert. opp. ∠s)

(b)Answer:

x = 137

(corr. ∠s,

AB \parallel CD

)[1]

x = 137

(corr. ∠s,

AB \parallel CD

)

(c)Answer:

x = 102

[3]

Draw the line

EF

through

E

, parallel to

AB

and

CD

, pointing towards

A

and

C

. It splits

x^\circ

into

\angle BEF

and

\angle FED

\angle BEF = 180^\circ - 112^\circ

\angle BEF = 68^\circ

(int. ∠s,

AB \parallel EF

)

\angle FED = 180^\circ - 146^\circ

\angle FED = 34^\circ

(int. ∠s,

CD \parallel EF

)

x = 68 + 34

x = 102

Practice questions by skill

Sec 1 Maths Angles and parallel lines worksheet with answers

In the print window, choose Save as PDF to download it.

Need the formulas first? Read the Angles and parallel lines notes. Or practise it online with step-by-step help when you get one wrong.

Answers and worked solutions

Question 1

Answer:

x = 122

(vert. opp. ∠s)[1]

x = 122

(vert. opp. ∠s)

Question 2

Answer:

x = 97

(supplementary ∠s)[2]

x^\circ + 83^\circ = 180^\circ

x = 180 - 83

x = 97

(supplementary ∠s)

Question 3

Answer:

x = 93

[3]

Draw the line

EF

through

E

, parallel to

AB

and

CD

, pointing towards

B

and

D

. It splits the angle

BED

inside the bend into

\angle BEF

and

\angle FED

\angle BEF = 38^\circ

(alt. ∠s,

AB \parallel EF

)

\angle FED = 28^\circ

(alt. ∠s,

CD \parallel EF

)

(3x + 15)^\circ + 38^\circ + 28^\circ = 360^\circ

(∠s at a pt.)

3x + 81 = 360

3x = 279

x = 93

Question 4

Answer: PS[3]

\angle PQS = \angle APQ

\phantom{\angle PQS} = 79^\circ

(alt. ∠s,

AB \parallel CD

)

\angle PSQ = \angle BPS

\phantom{\angle PSQ} = 34^\circ

(alt. ∠s,

AB \parallel CD

)

\angle QPS = 180^\circ - 79^\circ - 34^\circ

\phantom{\angle QPS} = 67^\circ

(∠s on a str. line)The largest angle is

79^\circ

, at

Q

, so the longest side is

PS

, opposite it.

Question 5

(a)Answer:

x = 71

[2]

x^\circ + 109^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 109

x = 71

(b)Answer:

x = 168

(∠s at a pt.)[2]

48^\circ + 90^\circ + 54^\circ + x^\circ = 360^\circ

x = 360 - 48 - 90 - 54

x = 168

(∠s at a pt.)

Question 6

(a)Answer:

x = 62

[2]

x^\circ + 118^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 118

x = 62

(b)Answer:

x = 96

(∠s at a pt.)[2]

129^\circ + x^\circ + 135^\circ = 360^\circ

x = 360 - 129 - 135

x = 96

(∠s at a pt.)

Question 7

(a)Answer:

x = 107

(∠s at a pt.)[2]

57^\circ + 101^\circ + 95^\circ + x^\circ = 360^\circ

x = 360 - 57 - 101 - 95

x = 107

(∠s at a pt.)

(b)Answer:

x = 35

[2]

3x - 25 = 2x + 10

(corr. ∠s,

AB \parallel CD

)

3x - 2x = 10 + 25

x = 35

Question 8

(a)Answer:

x = 113

[2]

Draw the line

EF

through

E

, parallel to

AB

and

CD

, pointing away from

A

and

C

. It splits

x^\circ

into

\angle BEF

and

\angle FED

\angle BEF = 47^\circ

(alt. ∠s,

AB \parallel EF

)

\angle FED = 66^\circ

(alt. ∠s,

CD \parallel EF

)

x = 47 + 66

x = 113

(b)Answer:

x = 64

(vert. opp. ∠s)[2]

\angle AOC = 28^\circ + 36^\circ

\angle AOC = 64^\circ

x = 64

(vert. opp. ∠s)

Question 9

(a)Answer:

x = 122

(vert. opp. ∠s)[1]

x = 122

(vert. opp. ∠s)

(b)Answer:

x = 137

(corr. ∠s,

AB \parallel CD

)[1]

x = 137

(corr. ∠s,

AB \parallel CD

)

(c)Answer:

x = 102

[3]

Draw the line

EF

through

E

, parallel to

AB

and

CD

, pointing towards

A

and

C

. It splits

x^\circ

into

\angle BEF

and

\angle FED

\angle BEF = 180^\circ - 112^\circ

\angle BEF = 68^\circ

(int. ∠s,

AB \parallel EF

)

\angle FED = 180^\circ - 146^\circ

\angle FED = 34^\circ

(int. ∠s,

CD \parallel EF

)

x = 68 + 34

x = 102