Post on 04-Jun-2018
8/14/2019 Angle Properties (Core).pdf
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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]
8/14/2019 Angle Properties (Core).pdf
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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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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]
8/14/2019 Angle Properties (Core).pdf
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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
NOT TO
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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]
8/14/2019 Angle Properties (Core).pdf
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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]
8/14/2019 Angle Properties (Core).pdf
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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
NOT TO
SCALE
ABis parallel to CD.
Calculate the value ofx.
Answer x = [3]
8/14/2019 Angle Properties (Core).pdf
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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]
8/14/2019 Angle Properties (Core).pdf
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7
12 (a) Find the value ofx.
x
51
NOT TO
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Answer(a) x = [1]
(b) EFis a diameter of the circle.
Find the value ofy.
y
63E
F
NOT TO
SCALE
Answer(b) y = [1]
(c) Find the value ofzin this isosceles triangle.
z
48 NOT TO
SCALE
Answer(c) z = [1]
8/14/2019 Angle Properties (Core).pdf
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8
13O
A B
75
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(a) TriangleAOBis isosceles.OA= OB.
Calculate angle AOB.
Answer(a)Angle AOB= [1]
(b)O
A B
NOT TO
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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]
8/14/2019 Angle Properties (Core).pdf
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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
NOT TO
SCALE
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]
8/14/2019 Angle Properties (Core).pdf
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10
15 (a)
A B
C
D E
110
NOT TO
SCALE
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]
8/14/2019 Angle Properties (Core).pdf
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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
NOT TO
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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]
8/14/2019 Angle Properties (Core).pdf
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18
OT
A
U
C
B
NOT TO
SCALE
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
8/14/2019 Angle Properties (Core).pdf
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20
OA
D
C
B
y
x
55
NOT TO
SCALE
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
8/14/2019 Angle Properties (Core).pdf
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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
8/14/2019 Angle Properties (Core).pdf
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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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24
157
84 x
NOT TOSCALE
Find the value ofx.
Answer x = [1]
15
8/14/2019 Angle Properties (Core).pdf
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Examiner's
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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
8/14/2019 Angle Properties (Core).pdf
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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
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8/14/2019 Angle Properties (Core).pdf
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28
A B
E
D
C
O
25o
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SCALE
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
8/14/2019 Angle Properties (Core).pdf
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Examiner's
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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
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M
Find the values ofx,yandz.
Answer(b) x = [1]
y = [2]
z = [2]
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8/14/2019 Angle Properties (Core).pdf
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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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