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```TOPIC#16
Geometry – Properties of Angles, Angle Properties of Polygons.
Q1.
Each interior angle of a regular polygon is 150°. Calculate the number of sides of the polygon.
Ans.
12
Q2.
The diagram shows part of a regular polygon with n sides.
Each interior angle of this polygon is 156°.
Find
(a)
the value of n,
(b)
ˆ ,
ACD
(c)
ˆ .
Ans.
(a)
15
Q3.
The diagram shows part of a regular polygon with n sides. Each interior angle of this polygon
(b)
ˆ  144
ACD
(c)
ˆ  24
is 162°.
Find
Ans.
(a)
the value of n,
(b)
ˆ ,
ACD
(c)
ˆ .
(a)
20
(b)
ˆ  153
ACD
(c)
ˆ  18
Compiled By : Sir Rashid Qureshi
www.levels.org.pk
1
TOPIC#16
Geometry – Properties of Angles, Angle Properties of Polygons.
Q4.
In the diagram, EAF is a straight line and AB is parallel to CD .
ˆ and CAB
ˆ  58.
AB bisects FAC
Find the value of
(a)
x,
(b)
y.
Ans.
(a)
x = 64,
Q5.
(a)
The interior angle of a regular polygon is 160°. How many sides does it have?
(b)
ABCDE ……. is part of a regular polygon which has interior angles of 160°.
(b)
y = 58
CDLM is a square.
Find
Ans.
Q6.
(i)
the value of x ,
(ii)
the value of y .
(a)
18 sides
(b)
(i)
(a)
In a diagram, ABCD is a parallelogram. ADE and BFE are straight lines.
x = 70
AF = BF.
(ii)
y = 105
ˆ  54 and CBF
ˆ  57
ABF
Find the value of
(i)
t,
(ii)
u,
(iii)
x,
(iv)
y.
Compiled By : Sir Rashid Qureshi
www.levels.org.pk
2
TOPIC#16
Geometry – Properties of Angles, Angle Properties of Polygons.
Ans.
Q7.
(a)
(i)
t = 69
(ii)
u = 57
(iii)
x = 72
(iv)
y = 15
alt. s
ˆ  34 and ABC
ˆ  42
DAC
In the diagram, BCD is a straight line. AD = AC ,
Find
(i)
ˆ ,
(ii)
ˆ ,
BAC
(iii)
the reflex angle ABC .
ˆ  31
BAC
(a)
ˆ  73
(c)
reflex ABC  318
(a)
Three of the angles of a quadrilateral are each 95°. Find the fourth angle.
(b)
Each interior angle of a regular polygon is 165°. How many sides has the polygon?
Ans.
(a)
75°
Q9.
ˆ  140 .
AB and BC are adjacent sides of a regular polygon. ABC
Ans.
Q8.
(b)
(b)
24
(a)
Calculate the number of sides of the polygon.
(b)
CB and BD are adjacent sides of a congruent regular
ˆ
polygon. Calculate ABD
Ans.
(a)
9
Q10.
(b)
ˆ  80
ABD
Aˆ  x, Bˆ  2 x, Cˆ  3x and Dˆ  4 x
(a)
Find x.
(b)
Explain why AB is parallel to DC.
Compiled By : Sir Rashid Qureshi
www.levels.org.pk
3
TOPIC#16
Geometry – Properties of Angles, Angle Properties of Polygons.
Ans.
(a)
x = 36°
(b)
ˆ  36  144  180
Aˆ  D
Since angles A and D are supplementary.
 AB \ \ DC
Q11.
In the diagram, the lines BA, DC and EF are parallel.
ˆ  115.
ˆ  140 and BCF
ABC
Find
Ans.
(a)
140°
Q12.
The diagram represents a framework.
BC = 1.3m,
(b)
BD = 1.9m
and
(a)
ˆ ,
DCB
(b)
ˆ ,
DCF
(c)
ˆ .
EFC
105°
(c)
75°
(c)
ˆ
BDC=41.6
BE = 1.5m,
ˆ  76 , BAE
ˆ  68 and BED
ˆ  90.
BCD
Calculate
(a)
ˆ ,
DBE
(b)
AE ,
(c)
ˆ .
BDC
Ans.
(a)
ˆ  37.9
DBE
Q13.
In the diagram, the circle, centre O , passes through A, B and C .
(b)
AE  0.606m
AC is a diameter of the circle and the line TAS is the tangent at A .
Compiled By : Sir Rashid Qureshi
www.levels.org.pk
4
TOPIC#16
Geometry – Properties of Angles, Angle Properties of Polygons.
ACB  34,
TA  3cm
and
TC  5cm.
(a)
Find BAC
(b)
Calculate the radius of the circle.
Ans.
(a)
BAC  56
Q14.
In the diagram, ABCD is part of a regular polygon.
(b)
Each interior angle is 165°.
(a)
How many sides does this polygon have?
(b)
ABPQ is part of another regular polygon.
This polygon has 12 sides.
Calculate x.
Ans.
Q15.
(a)
number of sides = 24
(b)
x = 45°
(a)
In the diagram, LMN is parallel to PQR.
Angle PQM = 124° and MQ = MR.
Find
(i)
x,
(ii)
y,
Compiled By : Sir Rashid Qureshi
www.levels.org.pk
5
TOPIC#16
Geometry – Properties of Angles, Angle Properties of Polygons.
Ans.
(a)
(i)
x° = 56°
Compiled By : Sir Rashid Qureshi
(b)
y° = 68°
www.levels.org.pk
6
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