In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.

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Solution

In the given figure,,,and

We need to find the value of x and y

Here, asand BD is the transversal, so according to the property, “alternate interior angles are equal”, we get

Similarly, as and DF is the transversal

(Using 1)

Further, EGH is a straight line. So, using the property, angles forming a linear pair are supplementary

Also, using the property, “an exterior angle of a triangle is equal to the sum of the two opposite interior angles”, we get,

In with as its exterior angle

Thus,

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