Sec 1 G1 Maths Angles worksheet with answers

A free Sec 1 G1 Maths worksheet on angles: 11 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 G1 Maths worksheet: Angles

Total: 30 marksSuggested time: 50 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,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer[1]

In the diagram,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer[1]

In the diagram,

AOB

is a straight line. Find

x

Answer[2]

In the diagram,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer[2]

\angle ABC

and

\angle PQR

are complementary angles. Find

x

Answer[2]

In the diagram,

AOB

is a straight line. Find

x

Answer[2]

In the diagram,

AB

is parallel to

CD

, and the straight line

EF

cuts them at

P

and

Q

. Find

x

Answer[2]

In the diagram, the line segments

OA

OB

and

OC

meet at the point

O

. Find

x

Answer[2]

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)[1]

(b)In the diagram, the line segments

OA

OB

OC

and

OD

meet at the point

O

. Find

x

Answer (b)[2]

(c)In the diagram, the line segments

OA

OB

and

OC

meet at the point

O

. Find

x

Answer (c)[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)[1]

(b)

\angle ABC

and

\angle PQR

are supplementary angles. Find

x

Answer (b)[2]

(c)In the diagram,

AOB

is a straight line. Find

x

Answer (c)[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 straight lines

AB

and

CD

meet at

O

OE

is a straight line between

OA

and

OC

. Find

x

Answer (b)[2]

(c)

\angle ABC

and

\angle PQR

are complementary angles. Find

x

Answer (c)[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

x = 66

(corr. ∠s,

AB \parallel CD

)[1]

\angle APQ = 66^\circ

(vert. opp. ∠s)

x = 66

(corr. ∠s,

AB \parallel CD

)

Question 2

Answer:

x = 61

(corr. ∠s,

AB \parallel CD

)[1]

x = 61

(corr. ∠s,

AB \parallel CD

)

Question 3

Answer:

x = 57

(∠s on a str. line)[2]

74^\circ + x^\circ + 49^\circ = 180^\circ

x = 180 - 74 - 49

x = 57

(∠s on a str. line)

Question 4

Answer:

x = 48

[2]

x^\circ + 132^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 132

x = 48

Question 5

Answer:

x = 73

(complementary ∠s)[2]

x^\circ + 17^\circ = 90^\circ

x = 90 - 17

x = 73

(complementary ∠s)

Question 6

Answer:

x = 71

(∠s on a str. line)[2]

41^\circ + 68^\circ + x^\circ = 180^\circ

x = 180 - 41 - 68

x = 71

(∠s on a str. line)

Question 7

Answer:

x = 66

[2]

x^\circ + 114^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 114

x = 66

Question 8

Answer:

x = 110

(∠s at a pt.)[2]

104^\circ + x^\circ + 146^\circ = 360^\circ

x = 360 - 104 - 146

x = 110

(∠s at a pt.)

Question 9

(a)Answer:

x = 132

(corr. ∠s,

AB \parallel CD

)[1]

x = 132

(corr. ∠s,

AB \parallel CD

)

(b)Answer:

x = 66

(∠s at a pt.)[2]

x^\circ + 101^\circ + 54^\circ + 139^\circ = 360^\circ

x = 360 - 101 - 54 - 139

x = 66

(∠s at a pt.)

(c)Answer:

x = 83

(∠s at a pt.)[2]

117^\circ + x^\circ + 160^\circ = 360^\circ

x = 360 - 117 - 160

x = 83

(∠s at a pt.)

Question 10

(a)Answer:

x = 104

(corr. ∠s,

AB \parallel CD

)[1]

x = 104

(corr. ∠s,

AB \parallel CD

)

(b)Answer:

x = 76

(supplementary ∠s)[2]

x^\circ + 104^\circ = 180^\circ

x = 180 - 104

x = 76

(supplementary ∠s)

(c)Answer:

x = 145

(∠s on a str. line)[2]

35^\circ + x^\circ = 180^\circ

x = 180 - 35

x = 145

(∠s on a str. line)

Question 11

(a)Answer:

x = 48

[2]

x^\circ + 132^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 132

x = 48

(b)Answer:

x = 117

(vert. opp. ∠s)[2]

\angle AOC = 63^\circ + 54^\circ

\angle AOC = 117^\circ

x = 117

(vert. opp. ∠s)

(c)Answer:

x = 47

(complementary ∠s)[2]

x^\circ + 43^\circ = 90^\circ

x = 90 - 43

x = 47

(complementary ∠s)

Sec 1 G1 Maths Angles worksheet with answers

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

Or practise it online with step-by-step help when you get one wrong.

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)[1]

(b)In the diagram, the line segments

OA

OB

OC

and

OD

meet at the point

O

. Find

x

Answer (b)[2]

(c)In the diagram, the line segments

OA

OB

and

OC

meet at the point

O

. Find

x

Answer (c)[2]

Answers and worked solutions

Question 1

Answer:

x = 66

(corr. ∠s,

AB \parallel CD

)[1]

\angle APQ = 66^\circ

(vert. opp. ∠s)

x = 66

(corr. ∠s,

AB \parallel CD

)

Question 2

Answer:

x = 61

(corr. ∠s,

AB \parallel CD

)[1]

x = 61

(corr. ∠s,

AB \parallel CD

)

Question 3

Answer:

x = 57

(∠s on a str. line)[2]

74^\circ + x^\circ + 49^\circ = 180^\circ

x = 180 - 74 - 49

x = 57

(∠s on a str. line)

Question 4

Answer:

x = 48

[2]

x^\circ + 132^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 132

x = 48

Question 5

Answer:

x = 73

(complementary ∠s)[2]

x^\circ + 17^\circ = 90^\circ

x = 90 - 17

x = 73

(complementary ∠s)

Question 6

Answer:

x = 71

(∠s on a str. line)[2]

41^\circ + 68^\circ + x^\circ = 180^\circ

x = 180 - 41 - 68

x = 71

(∠s on a str. line)

Question 7

Answer:

x = 66

[2]

x^\circ + 114^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 114

x = 66

Question 8

Answer:

x = 110

(∠s at a pt.)[2]

104^\circ + x^\circ + 146^\circ = 360^\circ

x = 360 - 104 - 146

x = 110

(∠s at a pt.)

Question 9

(a)Answer:

x = 132

(corr. ∠s,

AB \parallel CD

)[1]

x = 132

(corr. ∠s,

AB \parallel CD

)

(b)Answer:

x = 66

(∠s at a pt.)[2]

x^\circ + 101^\circ + 54^\circ + 139^\circ = 360^\circ

x = 360 - 101 - 54 - 139

x = 66

(∠s at a pt.)

(c)Answer:

x = 83

(∠s at a pt.)[2]

117^\circ + x^\circ + 160^\circ = 360^\circ

x = 360 - 117 - 160

x = 83

(∠s at a pt.)

Question 10

(a)Answer:

x = 104

(corr. ∠s,

AB \parallel CD

)[1]

x = 104

(corr. ∠s,

AB \parallel CD

)

(b)Answer:

x = 76

(supplementary ∠s)[2]

x^\circ + 104^\circ = 180^\circ

x = 180 - 104

x = 76

(supplementary ∠s)

(c)Answer:

x = 145

(∠s on a str. line)[2]

35^\circ + x^\circ = 180^\circ

x = 180 - 35

x = 145

(∠s on a str. line)

Question 11

(a)Answer:

x = 48

[2]

x^\circ + 132^\circ = 180^\circ

(int. ∠s,

AB \parallel CD

)

x = 180 - 132

x = 48

(b)Answer:

x = 117

(vert. opp. ∠s)[2]

\angle AOC = 63^\circ + 54^\circ

\angle AOC = 117^\circ

x = 117

(vert. opp. ∠s)

(c)Answer:

x = 47

(complementary ∠s)[2]

x^\circ + 43^\circ = 90^\circ

x = 90 - 43

x = 47

(complementary ∠s)