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Sample Paper 4Section D(Questions 23 to 30 carry 4 marks each)ifference is 8°. Find the number of sides of the polygon. |
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Answer» Given smallest interior angle is 52° Common difference is 8° Each of the interior angle increases by 8° Hence exterior decreases by 8°Exterior angle corresponding to 52° = 180° - 52° = 128° Next exterior angle = 128° - 8°=120° and so onHence the AP is 128°, 120°… Sum of exterior angles of a polygon = 360° That is 128° + 120° +… n terms = 360°Sum of n terms of AP is (n/2)[2a + (n – 1)d]Hence, 360° = (n/2)[2(128°) + (n – 1)(-8°)]720 = n(256 – 8n + 8)8n2– 264n + 720 = 0n2– 33n + 90 = 0n2– 30n – 3n + 90 = 0n(n – 30) – 3(n + 30) = 0(n – 30)(n – 3)=0n – 30 = 0 or n – 3 = 0Thus n = 30 or n = 3But n cannot be 30 as the exterior angles become negative after few terms.Thus n = 3 |
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