Question

In figure, rays AB and CD intersect at O.


i. Determine $y$ when $x={60}^{\circ }$

Answer 1

$\text{Given}x={60}^{\circ },\angle AOC=2x\text{and}\angle BOC=y$

As, AB is a straight line
$\therefore \angle AOC+\angle BOC={180}^{\circ }\left(\text{Linear pair}\right)$

$2x+y={180}^{\circ }$

$2\left({60}^{\circ }\right)+y={180}^{\circ }$

$y={180}^{\circ }-{120}^{\circ }$

$y={60}^{\circ }$