Question

$ABCD$ is a cyclic quadrilateral. A circle passing through $A$ and $B$ meets $AD$ and $BC$ in the points $E$ and $F$ respectively. If $\angle ABF={85}^o$, then the value of $\angle ADC$ is equal to:

• A. ${80}^o$
• B. ${85}^o$
• C. ${90}^o$
• D. ${95}^o$

Answer 1

The correct option is D ${95}^o$

$\Rightarrow$ In given figure, ABCD is a cyclic quadrilateral. (Given)

$\Rightarrow$ $\angle$ABF = 85${}^{\circ }$ (Given)

$\Rightarrow$ $\angle$ABF + $\angle$ADC = 180${}^{\circ }$ (opposite angles of cyclic quadrilateral are supplementary.)

$\Rightarrow$ 85${}^{\circ }$ + $\angle$ADC = 180${}^{\circ }$

$\Rightarrow$ $\angle$ADC = 180${}^{\circ }$ - 85${}^{\circ }$

$\therefore$ $\angle ADC={95}^{\circ }$