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°
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 \(180^\circ)\)
\(\Rightarrow\) \(\angle C\) \(=180^\circ-\angle A\)
\(=180^\circ-45^\circ\) \((\because\) \(\angle A=45^\circ)\)
= \(135^\circ\)