Question

If ABCD is a cyclic quadrilateral and $\angle A=120°-x°,$ then $\angle C=$ .

• A. 60° + x°
• B. 90° + x°
• C. 60° - x°
• D. 90° - x°

Answer 1

The correct option is A 60° + x°

Given: ABCD is a cyclic quadrilateral
$\angle A=120°-x°$


We know that the sum of opposite angles of a cyclic quadrilateral is 180${}^{\circ }$.
$\Rightarrow \angle A+\angle C=180°$
$\Rightarrow \angle C=180°-\angle A$
$\Rightarrow \angle C=180°-(120-x)°$
$\Rightarrow \angle C=180°-120°+x°=60°+x°$