Question

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

Answer 1

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°