Question

In the given figure, O is the centre of the circle and $\angle DAB={50}^{\circ }.$ Calculate the values of x and y.

Answer 1

ANSWER:
O is the centre of the circle and ∠ DAB = 50 ° .
OA = OB (Radii of a circle)
⇒ ∠ OBA = ∠ OAB = 50 °
In Δ OAB, we have:
∠ OAB + ∠ OBA + ∠ AOB = 180 °
⇒ 50 ° + 50 ° + ∠ AOB = 180 °
⇒ ∠ AOB = (180 ° – 100 °) = 80 °
Since AOD is a straight line, we have:
∴ x = 180 ° – ∠ AOB
= (180 ° – 80 °) = 100 °
i.e., x = 100 °
The opposite angles of a cyclic quadrilateral are supplementary.
ABCD is a cyclic quadrilateral.
Thus, ∠ DAB + ∠ BCD = 180 °
∠ BCD = (180 ° – 50 ° ) = 130 °
∴ y = 130 °
Hence, x = 100 ° and y = 130 °