Question

In the given figure, AB||CD. Find the values of x,y and z.

Answer 1

AB ∥ CD and let EF and EG be the transversals.

Now, AB ∥ CD and EF is the transversal.

Then,

∠AEF =∠EFG Alternate Angles

⇒ y° = 75°

Also,

∠EFC + ∠EFD = 180° Since CFD is a straight line

⇒ x + y = 180

⇒ x + 75 = 180

⇒ x = 105

And,

∠EGF + ∠EGD = 180° Since CFGD is a straight line

⇒ ∠EGF + 125 = 180

⇒ ∠EGF = 55°

We know that the sum of angles of a triangle is 180°

∠EFG + ∠GEF + ∠EGF = 180°

⇒ y + z + 55 = 180

⇒ 75 + z + 55 = 180

⇒ z = 50

∴x = 105, y = 75 and z = 50