Question

$ABCD$ is a cyclic quadrilateral $AE$ is drawn parallel to $CD$ and $BA$ is produced. If $\angle ABC={92}^{\circ }$ and $\angle FAE={20}^{\circ },$ then $\angle BCD=$

• A. ${88}^{\circ }$
• B. ${108}^{\circ }$
• C. ${115}^{\circ }$
• D. ${72}^{\circ }$

Answer 1

Answer: (B)

${108}^{\circ }$

We know that exterior angle of a cyclic quadrilateral is equal to the interior opposite angle

Also, in a cyclic quadrilateral $ABCD,$ sum of opposite angles is ${180}^{\circ }$

$\angle ADC+\angle ABC={180}^{\circ }$

$\angle ADC+{92}^{\circ }$ = ${180}^{\circ }$

$\angle ADC={88}^{\circ }$

$\angle EAD=\angle ADC={88}^{\circ }$ (Alternate interior angles of parallel lines $CD$ and $AE$)

$\angle FAD={20}^{\circ }$+${88}^{\circ }={108}^{\circ }$

$\angle BCD=\angle FAD={108}^{\circ }$ (Exterior angle of a cyclic quadrilateral)