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Question
The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5: 6: 7.
(i) Using the formula, find the sum of the interior angles of the pentagon.
(ii) Write the value of ∠A + ∠E
(iii) Find angles B, C and D.
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Solution
(i) Sum of interior angles of the pentagon
= (5 - 2) × 180°
= 3 × 180° = 540° ...[∵ sum for a polygon of x sides = (x - 2) × 180°]
(ii) Since AB || ED
∴ ∠A + ∠E = 180°
(iii) Let ∠B = 5x , ∠C = 6x , ∠D = 7x
∴ 5x + 6x + 7x + 180° = 540° ...(∠A + ∠E = 180°) (Proved in (ii))
18x = 540° - 180°
⇒ 18x = 360°
⇒ x = 20°
∴ ∠B = 5 × 20° = 100° , ∠C = 6 × 20 = 120°
∠D = 7 × 20 = 140°
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