In figure, if lines l and m are parallel, then x = - Vidyadip

MCQ

In figure, if lines l and m are parallel, then x =

A
20°
B
45°
C
65°
D
85°

✓

Answer

45°
Solution:

From figure,
$\angle\text{ABD}=\angle\text{CDF}$ [Correspondence angles]
$\Rightarrow\ \angle\text{CDF}=65^\circ$
Now,
$\angle\text{FDE}=180^\circ-\angle\text{CDF}=180^\circ-65^\circ$
$\Rightarrow\ \angle\text{FDE}=115^\circ$
In $\triangle\text{EDF},$
$\angle\text{FDE}+\angle\text{DEF}+\angle\text{EFD}=180^\circ$
$\Rightarrow\ 115^\circ+\text{x}+20^\circ=180^\circ$ [Sum of all interior angles of a $\triangle$ as 180°]
$\Rightarrow\ \text{x}=180^\circ-20^\circ-115^\circ=45^\circ$

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