Question
In a Pentagon ABCDE, ∠A = 110° and ∠B =
140° and ∠D = ∠E. Side AB and DC were extended and meet at the point P such that ∠BPC = 90°. Find the value of ∠E?Solution
Meeting point of AB and DC is P. ∠BPC = 90° ∠B = 140°, ∠PBC = 180°- 140°.= 40° ∠BCP = 90° - 40° = 50° ∠BCD = 180° - 50° = 130° Let ∠D = ∠E = x Interior Angles of polygon = (n – 2) × 180 Interior Angels of pentagon = (5 – 2) × 180 = 540 ∠A + ∠B + ∠ C + ∠D + ∠E = 540 110° + 140° + 130° + x + x = 540 2x = 540 – 380 x = 80° ∠E = 80°
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