Question

In the figure, rays AB and CD intersect at O.
(i) Determine y when x= ${60}^{\circ }$
(ii) Determine x when y= ${40}^{\circ }$

Answer 1

In the figure,
AB is a line
$\therefore 2x+y={180}^0$ (Linear pair)
(i) If x = ${60}^0$, then
$2\times {60}^0+y={180}^0\Rightarrow {120}^0+y={180}^0\therefore y={180}^0-{120}^0={60}^0$
(ii) If y = ${40}^0$, then
$2x+{40}^0={180}^0\Rightarrow 2x={180}^0-{40}^0={140}^0\Rightarrow x=\frac{{140}^0}{2}={70}^0\therefore x={70}^0$