If ABCD is a cyclic quadrilateral, then ∠A + ∠C = 

Correct Answer - 82.8 `cm^(2)`

Correct option is   A) rectangle

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 \(180^\circ)\) \(\Rightarrow\) \(\angle C\) \(=180^\circ-\angle A\) \(=180^\circ-45^\circ\) ...

Correct option is (D) 72°, 108° Let angles are 2x and 3x. Then 2x+3x = \(108^\circ\)   \((\because\) Sum of opposite angles in a cyclic quadrilateral is \(180^\circ)\) \(\Rightarrow\) 5x = \(108^\circ\) \(\Rightarrow\) x = \(\frac{180^\circ}5=36^\circ\) \(\therefore\) \(2x=72^\circ\;and\;3x=108^\circ\) Hence, required angles are \(72^\circ\;and\;108^\circ.\)

Correct option is (A) Cyclic If the sum of the pairs of opposite angles of a quadrilateral is \(180^\circ,\) then the quadrilateral is cyclic quadrilateral.

Correct option is (C) 160° \(\because\) Sum of all angles in a quadrilateral is \(360^\circ.\) \(\therefore\) In quadrilateral ABCD, \(\angle A+\angle B\) \(+\angle C+\angle D\) \(=360^\circ\) \(\Rightarrow\) \(200^\circ\) \(+\angle C+\angle D\) \(=360^\circ\)  \((\because\angle A+\angle B=200^\circ)\) \(\Rightarrow\) \(\angle C+\angle D\) \(=360^\circ-200^\circ=160^\circ\)