Find the size of each lettered angle in the following figure:

In given figure, AD || FE [Given]

⇒ 60° + y = 180° and x + 110° = 180° (∵ Sum of adjacent interior angle in trapezium = 180°)

⇒ y = 180° – 60° and x = 180° – 110°

⇒ y = 120° and x = 70°

Since, AB || DE [Given]

∠BAD = ∠ADE = 70° (Alternate angles are equal)

In quadrilateral ABCD,

⇒ ∠BAD + 75° + z + 130° = 360° (∵ Sum of angles of a quadrilateral = 360°)

⇒ 70° + 75° + z + 130° = 360°

⇒ 275° + z = 360°

⇒ z = 360° – 275° = 85°.

Hence, x = 70°, y = 120° and z = 85°.