1.

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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