78.

5. In the given figure, find the values of a, b, c and d. Given that ∠BCD = 43° and ∠BAE = 62°.

∠c = ∠BAE
| An exterior angle of a cyclic quadrilateral is equal to its interior opposite angle
⇒ ∠c = 62°    ...(1)
In ∆AEC,
∠ACE + ∠CAE + ∠d = 180°
| Angle sum property of a triangle
⇒    43° + 62° + ∠d = 180°
⇒    ∠d = 75° ...(2)
∠a + ∠d = 180°
| Opposite angles of a cyclic quadrilateral are supplementary
⇒ ∠a + 75° = 180°
⇒    ∠a = 105°    ...(3)
In ∆FDE,
∠c + (180° - ∠d) + ∠b = 180°
| Angle sum property of a triangle
⇒ 62° + (180° - 75°) + ∠b= 180°
⇒    ∠b = 13°