Question

In figure, lines $$ l $$ and $$ m $$ are parallel. Find $$ \angle x $$ and give reasons for your answer.

Answer 1

From figure, we can write
$$ x + x + \angle BPQ = 180^{\circ} $$ (straight angle)
$$ \Rightarrow 2x + \angle BPQ = 180^{\circ} $$
$$ \angle BPQ = 180^{\circ} - 2x $$...........(i)
$$ l || m $$
$$ \angle BPQ = 68^{\circ} $$ (alt angle)........(ii)
From equations (i) and (ii), we have
$$ 68^{\circ} = 180^{\circ} -2x $$
$$ \Rightarrow 2x = 180^{\circ} - 68^{\circ} $$
$$ \Rightarrow 2x = 112^{\circ} $$
$$ \Rightarrow x = 56^{\circ} $$