Q1. The difference between exterior angle of (n-1) sided regular polygon and exterior
angle of (n+2) sided regular polygon is 6. Find the value of ‘n’?
Q2. A garden is in the shape of a regular pentagon as shown in the figure:
There are 3 right angles and 2 equal obtuse angles with measure x. Find the value of x?
Q3. If the diagonals of a rhombus are of length 12 cm and 16 cm, then find:
(a) Side of rhombus
(b) Area of rhombus
Q4. Find the values of x, y and z in the figure shown:
Q5. Three of the exterior angles of a septagon are 32°, 55° and 61°. If each of the
remaining exterior angle of this septagon is p°, calculate the value of p.
Q6. In the figure shown, ABCD is a parallelogram and FBED is a square. What is the
perimeter of ABCD if BD = 6√2 and AB = 10 cm?
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Q7. A regular hexagon is inscribed in a circle of radius 7 cm, find the perimeter of
hexagon.
Q8. The ratio between the number of sides of two regular polygons is 2 : 3 and the ratio
between sum of their interior angles is 1 : 2. Find the number of sides in each polygon.
Q9. PQRS is a kite whose diagonals intersect at O. If
find PQR and PSR.
QPS = 120° and
QRS = 40°,
Q10. Using ruler and compass only, draw a parallelogram whose diagonals are 6 cm and
8 cm and which cut each other so that one pair of vertically opposite angles are equal to
60°.
Q11. ABCDEFGH is a regular octagon and an isosceles triangle CDX is such that CX = DX
and the triangle CDX is exterior to octagon ABCDEFGH. IF DCX = 65°, find the measure
of EDX.
Q12. ABCDE is a pentagon such that A = 110°, B = 145° and D=
and AB when produced meet at an angle of 75°, find BCD and E.
E. IF sides DC
Q13. In the figure shown, AIGEC is a pentagon. Find:
ICG.
AGC +
EAG +
CIE +
AEI +
Q14. In a quadrilateral two angles are equal. The third angle is equal to the sum of the
two equal angles. The fourth angle is 60° less than twice the sum of the other three
angles. Find the measures of the angles in the quadrilateral.
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Q15. In the figure shown, ABCD is a rhombus with square BCEF on top of it. If G is the
point of intersection of AC and DE, prove that AGD = 45°.
Q16. ABCD is an isosceles trapezium such that
2x°. Find the values of x, y and z.
A = 65°
B = z°,
C = y° and
D=
Q17. Prove that:
(a) The diagonals of a square cut each other at right angles
(b) The diagonals of an isosceles trapezium are equal
Q18. ABCD is a parallelogram and P and Q are points on diagonal BD such that AP || CQ.
Prove that P and Q are points of trisection of diagonal BD (i.e. BP = PQ = QD).
Q19. Using ruler and compass only, construct a rhombus in which length of diagonals is
10 cm and 8 cm respectively. Also, measure the side of the rhombus thus formed. Side of
the rhombus is=6.4
Answers:
A1. n=13
A2. 135°
A3. (a) 10 cm
(b) 96 cm2
A4. x= 21°, y = 67°, z = 113°,
A5. p = 53°
A6. 48 cm
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A7. 42 cm
A8. 4 , 6
A9.
PQR =
PSR = 100°
A10. Use properties of parallelogram
A11. 160°
A12.
BCD = 110° and
E = 87.5°
A13. 180°
A14. 35°, 35°, 70° and 220°
A15. Use properties of rhombus and square
A16. x= 57.5°, y = 115° and
z = 65°
A17. Use properties of trapezium and square
A18. Use properties of parallelogram
A19. Use properties of rhombus, Side of rhombus = 3 cm. Side of the rhombus is=6.4
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