1.

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

Answer»

Given that AB // DE, ∠CDE = 53°; 

∠BAC = 35° 

Now ∠E = 35°

( ∵ alternate interior angles)

Now in ∆CDE 

∠C + ∠D + ∠E = 180° 

(∵angle sum property, ACDE) 

∴ ∠DCE + 53° + 35° = 180° 

⇒ ∠DCE = 180° – 88° = 92°


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