In the given figure, O is the centre of a circle and ∠BOD = 150°.
Question:

In the given figure, O is the centre of a circle and BOD = 150°. Find the values of x and y.

Solution:

O is the centre of the circle and BOD = 150°.
Thus, reflex angle BOD = (360° – 150°) = 210°

Now, $x=\frac{1}{2}(\operatorname{reflex} \angle B O D)=\left(\frac{1}{2} \times 210^{\circ}\right)=105^{\circ}$

∴ x = 105°
Again, x + y = 180° (Opposite angles of a cyclic quadrilateral)
⇒ 105° + y = 180°
⇒ y = (108° – 105°)= 75°
∴ y = 75°
Hence, 
x = 105° and y = 75°

 

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