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Question
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 AB ||DE ,BD || FG , ∠FGH =125° and ∠B = 55°
We need to find the value of x and y
Here, as AB || DE and BD is the transversal, so according to the property, “alternate interior angles are equal”, we get
∠D = ∠B
∠D = 55° ............. (1)
Similarly, as BD || FG and DF is the transversal
∠D = ∠F
∠F = 55° (Using 1)
Further, EGH is a straight line. So, using the property, angles forming a linear pair are supplementary
∠FGE + ∠FGH = 180°
y + 125° = 180°
y = 180° - 125°
y = 55°
Also, using the property, “an exterior angle of a triangle is equal to the sum of the two opposite interior angles”, we get,
In ΔEFG with ∠ FGH as its exterior angle
ext. ∠FGH = ∠F + ∠E
125° = 55° + x
x = 125° - 55°
x = 70°
Thus, x = 70° and y = 55°
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