Question

What value of x would make AOB a line in figure, if $\angle AOC=4xand\angle BOC=(6x+{30}^{\circ })$?

Answer 1

If AOB is a line, then

$\angle AOB={180}^{\circ }$ ( a straight angle = ${180}^{\circ }$)

$\Rightarrow \angle AOC+\angle BOC={180}^{\circ }$

$\Rightarrow 4x+(6x+{30}^{\circ })={180}^{\circ }$

$\Rightarrow 10x+{30}^{\circ }={180}^{\circ }$

$\Rightarrow 10x={150}^{\circ }$

$\Rightarrow x={15}^{\circ }$