Question

If the ratio of opposite angles of a cyclic quadrilateral is 5:1, then the values of the angles is

• A. ${90}^{\circ },90\circ$
• B. ${150}^{\circ },{30}^{\circ }$
• C. ${135}^{\circ },{45}^{\circ }$
• D. ${160}^{\circ },{20}^{\circ }$

Answer 1

The correct option is B

${150}^{\circ },{30}^{\circ }$

The sum of opposite angles in a cyclic quadrilateral is ${180}^{\circ }$.

Let the angles be A and B

$\angle A:\angle B=5:1$

$\angle B+5\angle B={180}^{\circ }$

$\angle B={30}^{\circ }$

$\therefore \angle A={150}^{\circ }$