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In the figure, if AB || DE, ∠ BAC = 35° and ∠CDE = 53°, find ∠ DCE.

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In the given figure 

∠BAC = ∠CED [Alternate angles] 

⇒ ∠CED = 35° 

In ∆CDE, 

∠CDE + ∠DCE + ∠CED = 180° [Angle sum property of a triangle] 

⇒ 53° + ∠DCE + 35° = 180° 

⇒ ∠DCE + 88° = 180° 

⇒ ∠DCE = 180° – 88° = 92° 

Hence, ∠DCE = 92° Ans

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