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Question
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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