Question
Find $x$ in the following case:
✓
Answer
In the figure,
$\because$ Lines are parallel
$\therefore \angle 1+2 \mathrm{x}=20^{\circ}$ ........(alternate angles)
But $\angle 1+3 x+25^{\circ}=180^{\circ}$ ...........(linear pair)
$ \Rightarrow 2 \mathrm{x}+20^{\circ}+3 \mathrm{x}+25^{\circ}=180^{\circ} $
$ \Rightarrow 5 \mathrm{x}+45^{\circ}=180^{\circ} $
$ \Rightarrow 5 \mathrm{x}=180^{\circ}-45^{\circ}=135^{\circ} $
$ \therefore x=\frac{135^{\circ}}{5}=27^{\circ} $
$\because$ Lines are parallel
$\therefore \angle 1+2 \mathrm{x}=20^{\circ}$ ........(alternate angles)
But $\angle 1+3 x+25^{\circ}=180^{\circ}$ ...........(linear pair)
$ \Rightarrow 2 \mathrm{x}+20^{\circ}+3 \mathrm{x}+25^{\circ}=180^{\circ} $
$ \Rightarrow 5 \mathrm{x}+45^{\circ}=180^{\circ} $
$ \Rightarrow 5 \mathrm{x}=180^{\circ}-45^{\circ}=135^{\circ} $
$ \therefore x=\frac{135^{\circ}}{5}=27^{\circ} $
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