Q. 34.4( 234 Votes )

# In Fig. 6.41, if AB || DE, ∠ BAC = 35° and ∠ CDE = 53°, find ∠ DCE.

Answer :

**Given: AB parallel DE, ∠BAC = 35 ^{o}, ∠CDE = 53^{o}To Find: ∠DCE**

According to question,

∠BAC = ∠CED (Alternate interior angles)

Therefore,

∠CED = 35^{o}

Now, In Δ DEC,

∠DCE + ∠CED + ∠CDE = 180^{o} (Sum of the interior angles of the triangle)

∠DCE + 35^{o} + 53^{o} = 180^{o}

∠DCE + 88^{o} = 180^{o}

∠DCE = 92^{o}

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