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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 . ADC 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 ADC is 162°. Find Ans. (a) the value of n, (b) ˆ , ACD (c) ˆ . ADC (a) 20 (b) ˆ 153 ACD (c) ˆ 18 ADC 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 , ADC (ii) ˆ , BAC (iii) the reflex angle ABC . ˆ 31 BAC (a) ˆ 73 ADC (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. In the quadrilateral ABCD, (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) radius 2cm 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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