ABCDE is a five-sided figure with no two sides equal and the interior anglesa B, C, D and E are each 120°. Calculate the size of the interior angle at A, and prove AB=ED+DC.
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(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°
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