Question

in figure if AB||CD, <BAC=35° & <CDE=53° then <DCE is
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Answer 1

here angle BAE and angle CED are alternate angles hence of same measure hence angle CED=35°and measure of triangle is 180°hence angle DCE=92°

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Answer 2

Hello mate ☺

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Solution:

It is given that AB∥DE. Therefore, ∠BAC=∠DEC              (Alternate Interior Angles)

∠BAC=35°      (Given)

Therefore, ∠DEC=35°

In ∆DCE, we have

∠DEC+∠CDE+∠DCE=180°         (Sum of three angles of a triangle =180°)

⇒35°+53°+∠DCE=180°

⇒∠DCE=180°−35°−53°=92°

I hope, this will help you.☺

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