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Sum of Opposite Angles of a Cyclic Quadrilateral

In a cyclic q...

Question

In a cyclic quadrilateral ABCD, ∠A = (2x + 4)°, ∠B = (y + 3)°, ∠C = (2y + 10)°, ∠D = (4x − 5)°. Find the four angles.

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Solution

We know that the sum of the opposite angles of cyclic quadrilateral is .in the cyclic quadrilateral, angles and and angles and pairs of opposite angles

Therefore and

Taking

By substituting and we get

Taking

By substituting and we get

By multiplying equation by we get

By subtracting equation from we get

By substituting in equation we get

The angles of a cyclic quadrilateral are

Hence, the angles of cyclic quadrilateral ABCD are .

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Similar questions

In a cyclic quadrilateral ABCD, $∠ A = (2 x + 4)^{\circ}, ∠ B = (y + 3)^{\circ}, ∠ C = (2 y + 10)^{\circ}, ∠ D = (4 x - 5)^{\circ}$ . Find the four angles.

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