PROBLEMS ON CYCLIC QUADRILATERAL

Problem 1 :

Solution :

In a cyclic quadrilateral, sum of opposite angles are supplementary.

∠A + ∠C = 180˚

x + 110˚ = 180˚

x = 180˚ - 110˚

x = 70˚

Problem 2 :

Solution :

Opposite angles in cyclic quadrilateral are supplementary 

x + 130˚ = 180˚

x = 180˚ - 130˚

x = 50˚

Problem 3 :

Solution :

In cyclic quadrilateral, opposite angles are supplementary.

∠A + ∠C = 180˚

x + 115˚ = 180˚

x = 180˚ - 115˚

x = 65˚

Problem 4 :

Solution :

Since O is the center of the circle, OA and OB are radius of circle.

OA = OB, then ∠OBA = ∠OAB

x + 30˚ + 50˚ = 180˚

x + 80˚ = 180˚

x = 180˚ - 80˚

x = 100˚

Problem 5 :

Solution :

x + 135˚ = 180˚

x = 180˚ - 135˚

x = 45˚

Problem 6 :

Solution :

Since O is the center of the circle, OA and OB are radius of circle.

OA = OB, then ∠OBA = ∠OAB = 40

x + 40˚ + 15˚ = 180˚

x + 55˚ = 180˚

x = 180˚ - 55˚

x = 125˚

Problem 7 :

Solution :

x + 45˚ = 180˚

x = 180˚ - 45˚

x = 135˚

Problem 8 :

Solution :

∠A = 180˚ - 70˚

∠A = 110˚

x = 180˚ - 40˚ - 110˚

x = 30˚

Problem 9 :

Solution :

x + 60˚ + 85˚ = 180˚

x = 180˚ - 60˚ - 85˚

x = 180˚ - 145˚

x = 35˚

Problem 10 :

Solution :

x + 135˚ + 30˚ = 180˚

x + 165˚ = 180˚

x = 180˚ - 165˚

x = 15