Question

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

• A.
  ${108}^{\circ }$
• B.
  ${118}^{\circ }$
• C.
  ${98}^{\circ }$
• D.
  ${78}^{\circ }$

Answer 1

The correct option is A

${108}^{\circ }$
Let $\angle EAD=x$

Since,
$\overrightarrow{AE}||CDandADisatransversal.\therefore \angle EAD=\angle ADC=x\text{(Alternate angles)}$

$x+{92}^{\circ }={180}^{\circ }$

[$\therefore$ Sum of either pair of opposite angles of a cyclic quaadrilateral is ${180}^{\circ }$]

$\Rightarrow x={88}^{\circ }\angle BCD=x+{20}^{\circ }$

[$\because$ The exterior angle of a cyclic quadrrilateral is equal to interior opposite angle]

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

Hence, the correct answer is option (a)