Question

(a) Find the values of x the following figure if l is parallel to m and a is parallel to b.


(b) What is the value of x in the figure?

​​​​​​​[4 MARKS]

Answer 1

Each part: 2 Marks

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

Mark an angle 1 in the figure.

$\angle 1={80}^{\circ }$ [Since 'a' is parallel to 'b', they are corresponding angles]

Now,

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

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

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


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

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