5. In the given figure, find the values of a, b, c and d. Given that ∠BCD = 43° and ∠BAE = 62°.
2x = 150°
| The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any point on the remaining part of the circle
⇒ x = 75° ...(1)
x + ∠BCD = 180°
| ∵ ACD is a straight line
⇒ 75° + ∠BCD = 180°
⇒ ∠BCD = 105°
∵ BEDC is a cyclic quadrilateral
∴ ∠BCD + ∠BED = 180°
| Opposite angles of a cyclic quadrilateral are supplementary
⇒ 105° + y = 180°
⇒ y = 75° ...(2)
z = 2y
| The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any point on the remaining part of the circle
⇒ z = 2 × 75° = 150° ...(3)