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Mathematics

In the given figure, ABCD is a cyclic quadrilateral. The measure of its greatest angle is :

  1. 135°

  2. 140°

  3. 150°

  4. 160°

In the given figure, ABCD is a cyclic quadrilateral. The measure of its greatest angle is. Loci, RSA Mathematics Solutions ICSE Class 10.

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Answer

The sum of the opposite angles of a cyclic quadrilateral is 180°.

∠A + ∠C = 180°

y + 5y = 180°

6y = 180°

y = 30°

∠B + ∠D = 180°

3x + x = 180°

4x = 180°

x = 45°

∠A = y = 30°

∠C = 5y = 150°

∠D = x = 45°

∠B = 3x = 135°

Hence, option 3 is the correct option.

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