In the given figure, ∠ECB = 40° and ∠CEB = 105°. Then, ∠EAD = ?
(a) 50°
(b) 35°
(c) 20°
(d) 40°

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Solution

(b) 35°

∠AED = ∠BEC = 105° (Vertically opposite angles)
∠ADE = ∠ACB = 40° (Angles in the same segment)
In ΔAED, we have:
∠AED + ∠ADE + ∠EAD = 180°
⇒ 105° + 40° + ∠EAD = 180°
⇒ ∠EAD = (180° - 145° ) = 35°

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