In the given figure, AB and CD are parallel. m ∠BAE = 45°, m ∠BEC = 55°, m ∠AED = 70° and m ∠ECD = 20°. Find m ∠CED.
Explanation:
Construct a line EF parallel to both AB and CD.
∴ m ∠CEF = m ∠ECD = 20° (∵ ∠CEF and ∠ECD form a pair of Alternate angles)
Also, m ∠AEG = m ∠EAB = 45° (∵ ∠AEG and ∠EAB form a pair of Alternate angles)
∴ m ∠GED = 70° − 45° = 25°
But, m ∠GED + m ∠CED + m ∠CEF = 180°
∴ 25° + m ∠CED + 20° = 180°
∴ m ∠CED = 135°
Hence, option (d).
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