angle properties (core).pdf

8/14/2019 Angle Properties (Core).pdf

1/20

For

Examiner's

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1

1

2

ED F

A CB

a

b

52

NOT TO

SCALE

In the diagram linesACandDFare parallel andAE=EB.AngleAEB= 52.

(a) Write down the mathematical name for triangleAEB.

Answer(a) [1]

(b) Work out the value of a.

Answer(b) a= [1]

(c) Explain why a= b.

Answer(c) [1]

The exterior angle of a regular pentagon is 72.

(a) Write down the interior angle of a regular pentagon.

Answer(a) ............................................... [1]

(b)

The diagram shows three pentagons which fit together.

Uta thinks that three regularpentagons will fit together in the same way.

Explain how you know she is wrong.

Answer(b) ........................................................................................................................................

................................................................................................................................................... [1]


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2

3

O

E

A

C BD

58

x

y

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ACis a diameter of a circle, centre O.BCDis a tangent to the circle andEis a point on the circumference.AngleECD= 58.

Work out the value of

(a) x,

Answer(a) x = [2]

(b) y.

Answer(b) y = [2]

4

160160

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SCALE

The diagram shows part of a regular polygon.

Each interior angle of the polygon is 160.Calculate the number of sides of the polygon.

Answer [3]


3/20

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3

5 (a) Show that the sum of the interior angles of a regular pentagon is 540.

Answer(a)

[2]

(b)

x y

y76

B C

D

EA

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The diagram shows a pentagonABCDE.BCis parallel toAEand angle CDEis a right angle.

Find the values ofxandy.

Answer(b) x =

y = [3]


4/20

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4

6 (a) A quadrilateral has four sides of equal length and two pairs of equal angles.

Write down the mathematical name for this quadrilateral.

Answer(a) [1]

(b)

74

92

63

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Three of the angles in a quadrilateral are 63, 74 and 92.

Work out the size of the fourth angle.

Answer(b) [1]

7 (a) Draw an acute angle.

Label the acute angle with the letter a.

[1]

(b) Write down the mathematical name of angle b.

b

Answer(b) ............................................... [1]


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5

8

40

58

A B

C

D

NOT TO

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In the quadrilateralABCD,AB=ADand CB= CD.

AngleBAD= 40 and angle CBD= 58.

(a) Calculate

(i) angleABD,

Answer(a)(i) AngleABD= [1]

(ii) angleBCD.

Answer(a)(ii) AngleBCD= [1]

(b) Write down the mathematical name for the quadrilateralABCD.

Answer(b) [1]

9

A B

C D

2x

5x x

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SCALE

ABis parallel to CD.

Calculate the value ofx.

Answer x = [3]


6/20

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6

10

A

C

D

B E115

20

yx

NOT TOSCALE

In the diagram,ABis parallel to CDE.Find the value of

(a) x,

Answer(a) x = [1]

(b) y.

Answer(b) y = [2]

11

75 x

2x2x

NOT TO

SCALE

(a) For the diagram above, write down an equation inx.

Answer(a) [1]

(b) Solve your equation.

Answer(b) x = [2]


7/20

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7

12 (a) Find the value ofx.

x

51

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Answer(a) x = [1]

(b) EFis a diameter of the circle.

Find the value ofy.

y

63E

F

NOT TO

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Answer(b) y = [1]

(c) Find the value ofzin this isosceles triangle.

z

48 NOT TO

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Answer(c) z = [1]


8/20

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8

13O

A B

75

NOT TO

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(a) TriangleAOBis isosceles.OA= OB.

Calculate angle AOB.

Answer(a)Angle AOB= [1]

(b)O

A B

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75

ABis one side of a regular polygon with nsides.

(i) Calculate n.

Answer(b)(i) n= [2]

(ii) Find the size of an interior angle of this polygon.

Answer(b)(ii) [1]


9/20

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9

14 (a)

A

C

B

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PointsA,Band Clie on the circumference of the circle shown above.

When angleBACis 90 write down a statement about the lineBC.

Answer(a) [1]

(b)

54

D

O

B

A

C

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Ois the centre of a circle and the lineABCis a tangent to the circle atB.Dis a point on the circumference and angleBOD= 54.

Calculate angleDBC.

Answer(b)AngleDBC= [3]


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10

15 (a)

A B

C

D E

110

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In the diagram,ABis parallel toDE.AngleABC= 110.

Find angleBDE.

Answer(a) AngleBDE= [2]

(b)

t

y

z50

O

B

A T

NOT TO

SCALE

TAis a tangent atAto the circle, centre O.Angle OAB= 50.

Find the value of

(i) y,

Answer(b)(i)y= [1]

(ii) z,

Answer(b)(ii)z= [1]

(iii) t.

Answer(b)(iii) t= [1]


11/20

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16C

A

B

O

T24

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A, Band Care points on a circle, centre O.TAis a tangent to the circle at Aand OBTis a straight line.

ACis a diameter and angle OTA= 24.

Calculate

(a) angle AOT,

Answer(a)Angle AOT= [2]

(b) angle BOC,

Answer(b)Angle BOC= [1]

(c) angle OCB.

Answer(c)Angle OCB= [1]

11

17

81

8763

O

B

C

D

A

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(a) Calculate the size of angle AOB.

Answer(a)Angle AOB = ............................................... [1]

(b) What type of angle is angle AOB?

Answer(b) ............................................... [1]


12/20

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18

OT

A

U

C

B

NOT TO

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In the diagram, TAUis a tangent to the circle at A.

ABis a diameter of the circle and AC=BC.

Find

(a) angle BCA,

Answer(a)Angle BCA= [1]

(b) angle ABC,

Answer(b)Angle ABC= [1]

(c) angle CAU.

Answer(c)Angle CAU= [1]

19

x 79

57

NOT TO

SCALE

The diagram shows a quadrilateral.Work out the value ofx.

Answer x= [1]

12


13/20

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20

OA

D

C

B

y

x

55

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The diagram shows a circle, centre O, with diameterBC.ABis a tangent to the circle atBand angleBCD= 55.A straight line fromAmeets the circle atDand C.

Calculate the value of

(a) x,

Answer(a) x = [2]

(b) y.

Answer(b) y = [1]

21

45 26

xNOT TO

SCALE

Find the value ofx.

Answer x= [1]

13


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22

wp t

A

D C

B M

NOT TO

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3267

The diagram shows a quadrilateralABCDwithDCparallel toAB.

(a) Write down the geometrical name for a quadrilateral with only onepair of parallel sides.

Answer(a) [1]

(b) ABMis a straight line andDC=AC.

AngleDCA= 32 and angleACB= 67.

Find the values of p, tand w, giving a reason for each answer.

Answer (b) p= because

[2]

t= because

[2]

w = because

[2]

14


15/20

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23

P, Qand Rlie on a circle, centre O.

PRis a diameter and angle OQR= 55.

Find

(a) angle PQR,

Answer(a)Angle PQR= [1]

(b) angle ROQ,

Answer(b)Angle ROQ= [1]

(c) angle OPQ.

Answer(c)Angle OPQ= [1]

55

R

O

P

Q

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SCALE

24

157

84 x

NOT TOSCALE

Find the value ofx.

Answer x = [1]

15


16/20

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26 In the diagramABis parallel to CD.

Calculate the value of a.

A

B

C

D

a

5a

NOT TOSCALE

Answer a = [2]

25

O

C

A

B

S T

54NOT TO

SCALE

A,Band Clie on a circle, centre O. BCis a diameter and SCTis a tangent at C. AngleACB= 54.

Find

(a) angleBCT,

Answer(a)AngleBCT = [1]

(b) angle COA,

Answer(b)Angle COA = [1]

(c) angle CAB,

Answer(c)Angle CAB = [1]

(d) angleABC.

Answer(d)AngleABC = [1]

16


17/20

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T

P

W

Q R

S

38105

NOT TO

SCALE

The lines PSand QTintersect at W.

PQRis a straight line.Angle SPR= 38and angle TQR= 105.

Write down the size of the following angles.In each case give a reason for your answer.

(a) Angle PQW= because

[2]

(b) Angle PWQ= because

[2]

(c) Angle TWS= because

[2]

17

27


18/20

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28

A B

E

D

C

O

25o

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In the diagram,DEis a diameter of the circle, centre O.AEBis the tangent at the pointE. The lineDCBcuts the circle at C.

AngleDEC= 25.

(a) Write down the size of angleDCE.

Answer (a) AngleDCE = [1]

(b) Calculate the size of angle CDE.

Answer (b) AngleCDE = [2]

(c) Calculate the size of angleDBE.

Answer (c) AngleDBE = [2]

18


19/20

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29 (a) ABCDEis a regular polygon with centre O.

A

B

DE

O

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(i) What is the special name for the polygon?

Answer(a)(i) [1](ii) Calculate angleEOD.

Answer(a)(ii) AngleEOD= [2](iii) Calculate angleAED.

Answer(a)(iii) AngleAED= [2]

(b) In the diagram below,ABand CDare straight lines which intersect at M.LMNandPQRSare parallel straight lines.

Angle QMR= 35and angleBMN= 64.

64o

35o

xo

yo zo

P Q R S

L N

D B

A C

NOT TO

SCALE

M

Find the values ofx,yandz.

Answer(b) x = [1]

y = [2]

z = [2]

19


20/20

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30

63100

z

yxP

T

S R

Q

NOT TO

SCALE

(a) In the diagramPQis parallel to SR, and QRis parallel toPT.PQ= QR, anglePRS= 63 and angleRST= 100.

Find the value of

(i) x,

Answer(a)(i)x= [1]

(ii) y,

Answer(a)(ii)y=

[2]

(iii) z.

Answer(a)(iii)z=

[2]

(b) The shape of a flower bed is a regular octagon,ABCDEFGH, with sides of 4 metres.

Show that the interior angle of a regular octagon is 135.

Answer(b)(i)

[2]

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angle properties (core).pdf

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