Using the information, given in each of the following figures, find the values of a and b.

In △ CAE,

⇒ AC = CE (Given)

∴ ∠AEC = ∠EAC = x (let) [Angles opposite to equal sides are equal]

By angle sum property of triangle,

⇒ ∠AEC + ∠EAC + ∠ACE = 180

⇒ x + x + 68° = 180°

⇒ 2x = 180° - 68°

⇒ 2x = 112°

⇒ x = $\dfrac{112°}{2}$ = 56°

⇒ ∠AEC = ∠EAC = 56°.

Since, B, E and C are in a straight line.

∴ ∠BEA + ∠AEC = 180°

⇒ a + 56° = 180°

⇒ a = 180° - 56° = 124°.

In △ ABE,

By angle sum property of triangle,

⇒ ∠ABE + ∠BEA + ∠EAB = 180°

⇒ ∠ABE + 124° + 14° = 180°

⇒ ∠ABE + 138° = 180°

⇒ ∠ABE = 180° - 138° = 42°.

Since, AB || CD

⇒ b = ∠ABE = 42°. (Alternate angles are equal)

Hence, a = 124° and b = 42°.