Answer in Brief

Compute the value of x in the following figure:

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#### Solution

In the given problem, we need to find the value of x

In the given figure, ∠BAD = 52° and ∠DCE = 40°

Here,AB || CD and *AD *is the transversal, so ∠EDC and ∠BAD form a pair of alternate interior angles. Therefore, using the property, “alternate interior angles are equal”, we get,

∠EDC = ∠BAD

∠EDC = 52°

Further, applying angle sum property of the triangle

In ΔDEC

∠DEC + ∠DCE + ∠EDC = 180°

∠DEC + 40° + 52° = 180°

x + 92° = 180°

x = 180° - 92°

x = 88°

Therefore, x = 88°

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