In the figure (ii) given below, if ∠ACE = 43° and ∠CAF = 62°, find the values of a, b and c.

From figure,

∠CAE = ∠CAF = 62°

Since sum of angles in triangle is 180°.

In △ACE,

⇒ ∠CAE + ∠ACE + ∠CEA = 180°
⇒ 62° + 43° + ∠CEA = 180°
⇒ ∠CEA + 105° = 180°
⇒ ∠CEA = 180° - 105°
⇒ ∠CEA = 75°.

From figure,

⇒ ∠CEA + ∠DEF = 180° (As they are linear pair.)
⇒ 75° + ∠DEF = 180°
⇒ ∠DEF = 180° - 75°
⇒ ∠DEF = 105°.

ABDE is a cyclic quadrilateral as all of its vertices lie on the circumference of the circle.

Since exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

⇒ ∠ABD = ∠DEF = 105°
⇒ a = 105°.

Since sum of angles in triangle is 180°.

In △ABF,

⇒ ∠BAF + ∠ABF + ∠BFA = 180°
⇒ 62° + a + b = 180°
⇒ 62° + 105° + b = 180°
⇒ b + 167° = 180°
⇒ b = 180° - 167°
⇒ b = 13°

Since exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

⇒ ∠EDF = ∠BAE = 62°
⇒ c = 62°.

Hence, the value of a = 105°, b = 13° and c = 62°.