1.

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

Answer»

We are given that AB || DE

and ∠BAC = 35° and ∠CDE = 53°

AB || DE (given)

⇒ ∠BAE = ∠AED = 35°

(alternate angles)

Now in ∆CDE,

∠CDE + ∠E + ∠DCE = 180°

(angle sum property of a triangle)

⇒ 53° + 35° + ∠DCE = 180°

⇒ ∠DCE = 180° – 88° = 92°

⇒ ∠DCE = 92°

Hence, ∠DCE = 92°.


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