10. The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and ZB: ZC: ZD = 5:6:7. () Using formula, find the sum of interior angles of the pentagon.
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The figure given below shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5 : 6 : 7.
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asked May 27, 2019 in Class VIII Maths by muskan15 (-3,983 points)
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 formula, find the sum of interior angles of the pentagon.
(ii) Write the value of ∠A + ∠E
(iii) Find angles B, C and D
understanding shapes (including polygons)
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answered May 27, 2019 by navnit40 (-4,935 points)
(i) Sum of interior angles of the pentagon
= (5 – 2) × 180°
= 3 × 180° = 540° [∴ Sum for a polygon of a x sides = (x – 2) × 180°]
(ii) Since AB ∥ ED
∴ ∠A + ∠E = 180°
(iii) Let ∠B = 5x, ∠C = 6x and ∠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°
this is the answer