In figure, some angles have been marked with a, b, c and d. Find the measures of these angles.

We know that in a cyclic quadrilateral, the exterior angle formed by producing one side of a quadrilateral is equal to its interior opposite angle.

∴ a = 65° and c = 91°

We know that the pair of opposite angles of a cyclic quadrilateral is supplementary i.e. sum is 180°.

Firstly, a + d = 180°

⇒ 65° + d = 180°

⇒ d = 180° - 65°

∴ d = 115°

Similarly, b + c = 180°

⇒ b + 91° = 180°

⇒ b = 180° - 91°

∴ b = 89°

∴ a = 65°, b = 89°, c = 91° and d = 115°