Question

In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x. [3 Marks]

Answer 1

Given CD || EF
$\Rightarrow \angle CGH=\angle FHG$
(Alternate interior angles are equal)
$\Rightarrow \angle CGH=z$ [1 Mark]

Also,
$\angle CGI+\angle CGH={180}^{\circ }$
(Both form a linear pair)
$\Rightarrow y+z={180}^{\circ }$ (i)

Given y : z = 3 : 7
Let us consider y as 3k and z as 7k.
$y+z={180}^{\circ }$ (from (i))
$\Rightarrow 3k+7k={180}^{\circ }$ [1 Mark]
$\Rightarrow 10k={180}^{\circ }$
$\Rightarrow k={18}^{\circ }$

$\Rightarrow z=7k=7\left({18}^{\circ }\right)={126}^{\circ }$

Also, AB || CD
$x=z$
(Corresponding angles are equal)

$\Rightarrow x={126}^{\circ }$ [1 Mark]