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

As CDE is a straight line

∠ADE + ∠ADC = 180°

122° + ∠ADC = 180°

∠ADC = 180° – 122° = 58° … (i)

Internal ∠ABC = 360° – 140° = 220° … (ii)

Now, in quadrilateral ABCD we have

⇒ ∠ADC + ∠BCD + ∠BAD + ∠ABC = 360° (As sum of all angles in a quadrilateral is 360°.)

⇒ 58° + 53° + x + 220° = 360° [Using (i) and (ii)]

⇒ 331° + x = 360°

⇒ x = 360° – 331°

⇒ x = 29°

Hence, x = 29°