In the given figure, ABCD is a cyclic quadrilateral in which DC i… - Vidyadip

MCQ

In the given figure, $ABCD$ is a cyclic quadrilateral in which $DC$ is produced to $E$ and $CF$ is drawn parallel to $AB$ such that $\angle\text{ADC}=95^\circ$ and $\angle\text{ECF}=20^\circ.$ Then, $\angle\text{EAD}=?$

A
$95^\circ$
B
$85^\circ$
✓
$105^\circ$
D
$75^\circ$

✓

Answer

Correct option: C.

$105^\circ$

Since $ CF || AB, \angle\text{ABC}=\angle\text{BCF}=85^\circ$
$\angle\text{BAD}=\angle\text{BCE}$
$\Rightarrow\ \angle\text{BAD}=\angle\text{BCF}+\angle\text{ECF}$
$\Rightarrow\ \angle\text{BAD}=105^\circ$

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