MCQ
In the given figure, $AB || CD.$ If $\angle\text{CAB}=180^\circ$ and $\angle\text{EFC}=25^\circ$ then $\angle\text{CEF}=?$ 
- A$65^\circ$
- ✓$55^\circ$
- C$45^\circ$
- D$75^\circ$
✓
Answer
Correct option: B.
$55^\circ$
Since $AB || CD,$
$\Rightarrow\angle\text{ACE}=\angle\text{BAC}=80^\circ$
In $\triangle\text{CEF},$
$\angle\text{ACE}=\angle\text{CEF}+\angle\text{CFE}( $Exterior angle is equal to sum of the remote interior angles$)$
$\Rightarrow80^\circ=\angle\text{CEF}+25^\circ$
$\Rightarrow\angle\text{CEF}=55^\circ$
$\Rightarrow\angle\text{ACE}=\angle\text{BAC}=80^\circ$
In $\triangle\text{CEF},$
$\angle\text{ACE}=\angle\text{CEF}+\angle\text{CFE}( $Exterior angle is equal to sum of the remote interior angles$)$
$\Rightarrow80^\circ=\angle\text{CEF}+25^\circ$
$\Rightarrow\angle\text{CEF}=55^\circ$
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