Question

(a) Find the value of x, if l is parallel to m and a is parallel to b.


(b)Find the value of x.

[4 MARKS]

Answer 1

Each part: 2 Marks

(a) Given, $a\parallel b$ and $l\parallel m$

Mark an angle 1 in the figure.

$\angle 1={80}^{\circ }$ [Corresponding angles]

$\angle 1+\angle x={180}^{\circ }$ [Since $l\parallel m,\angle 1and\angle x$ are cointerior angles]

$\Rightarrow \angle x={180}^{\circ }-{80}^{\circ }$

$\Rightarrow \angle x={100}^{\circ }$


(b) $\angle 5=5x+35$ (Alternate angles)
${45}^{\circ }+\angle 5={180}^{\circ }$ (Linear pair)
$\angle 5={180}^{\circ }-{45}^{\circ }$
$={135}^{\circ }$

$\therefore 5x+35=135$
$\Rightarrow 5x=135-35=100$
$\Rightarrow x=\frac{100}{5}=20$