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The points A, B, C and D on a circle form a quadrilateral ABCD. If ∠A = 45° then measure of ∠C = A) 45° B) 135° C) 225° D) 315° |
Answer» Correct option is (B) 135° ABCD is a cyclic quadrilateral. \(\angle A\;\&\;\angle C\) are opposite angles in cyclic quadrilateral ABCD \(\therefore\) \(\angle A+\angle C\) \(=180^\circ\) \((\because\) Sum of opposite angles in a cyclic quadrilateral is \(180^\circ)\) \(\Rightarrow\) \(\angle C\) \(=180^\circ-\angle A\) \(=180^\circ-45^\circ\) \((\because\) \(\angle A=45^\circ)\) = \(135^\circ\) Correct option is B) 135° |
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