Question

In the given figure, AB || CD. Find the value of x.

Answer 1

Draw EF ∥ AB ∥ CD.

EF∥CD and CE is the transversal.

Then,

∠ECD + ∠CEF = 180° Angles on the same side of a transversal line are supplementary

⇒ 130° + ∠CEF = 180°

⇒ ∠CEF = 50°

Again, EF∥AB and AE is the transversal.

Then,

∠BAE + ∠AEF = 180° Angles on the same side of a transversal line are supplementary

⇒ x° + 20° + 50° = 180°

∠AEF = ∠AEC + ∠CEF

⇒ x° + 70° = 180°

⇒ x° = 110°

⇒ x = 110