Question

25. In the given figure, AB || DE and BD || FG such that ZABC = 50°
2FGH = 120°. Find the values of x and y.
В
с
В
F
50°
120°
Х
у
A
с
E
G
Н
D​

Answer 1

Answer:

From the figure we know that ∠FGH and ∠FGE form a linear pair of angles So we get ∠FGH + ∠FGE = 180o

By substituting the values 120o + y = 180o On further calculation y = 180o – 120o By subtraction y = 60o We know that AB || DF and BD is a transversal

From the figure we know that ∠ABC and ∠CDE are alternate angles So we get ∠ABC = ∠CDE = 50o We know that BD || FG and DF is the transversal From the figure we know that ∠EFG and ∠CDE are alternate angles So we get ∠EFG = ∠CDE = 50o We know that the sum of all the angles in triangle EFG is 180o. ∠FEG + ∠FGE + ∠EFG = 180o

By substituting the values we get x + y + 50o = 180o x + 60o + 50o = 180o On further calculation x = 180o – 60o – 50o By subtraction x = 180o – 110o x = 70o Therefore, the values of x = 70o and y = 60o.