In the given figure, AB | CD. If =180^ and =25^ then =? - Vidyadip

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)
$\Rightarrow80^\circ=\angle\text{CEF}+25^\circ$
$\Rightarrow\angle\text{CEF}=55^\circ$

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