Question

Two opposite angles of a cyclic quadrilateral are $4x^o$ and $5x^o$, then the value of $x^o$ is equal to

• A. $0^o$
• B. ${20}^o$
• C. ${30}^o$
• D. ${40}^o$

Answer 1

Answer: (B)

${20}^o$

Two opposite angles of a cyclic quadrilateral are $4x^{\circ }$ and $5x^{\circ }$. ---- (Given)

$\Rightarrow$ $4x^{\circ }$ + $5x^{\circ }$ = ${180}^{\circ }$ ---- (Sum of opposite angles of a cyclic quadrilateral is supplementary)

$\Rightarrow$ $9x^{\circ }$ = ${180}^{\circ }$

$\therefore$ $x^{\circ }$ =${20}^{\circ }$

Hence, the value of $x^{\circ }$ is ${20}^{\circ }$.