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Question
In a pentagon ABCDE, AB || ED and ∠B = 140°, ∠C = 2x° and ∠D = 3x°. Find ∠C and ∠D
Solution
Since AB || ED, we have
∠A + ∠E = 180°
Now,
∠A + ∠B + ∠C + ∠D + ∠E = (5 - 2) x 180°
⇒ (∠A + ∠E) + 140° + 2x + 3x = 3 x 180°
⇒ 180° + 140° + 5x = 540°
⇒ 320° + 5x = 540°
⇒ 5x = 220°
⇒ x = 44°
Hence,
∠C = 2x = 2 x 44° = 88°
∠D = 3x = 3 x 44° = 132°.
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