Question

In the figure, a is greater than b by one third of a right-angle. Find the values of a and b.

Answer 1

In the figure,
$\angle AOC+\angle BOC={180}^{\circ }$ (Linear pair)
$\Rightarrow a+b={180}^{\circ }$ ...(i)
But $a=b+\frac{1}{3}\times {90}^{\circ }=b+{30}^{\circ }$
$\Rightarrow a-b={30}^{\circ }$ ...(ii)
Adding (i) and (ii)
$2a={210}^{\circ }\Rightarrow a=\frac{{210}^{\circ }}{2}={105}^{\circ }$
and ${105}^{\circ }+b={180}^{\circ }\Rightarrow$ $b={180}^{\circ }-{105}^{\circ }$
$\therefore b={75}^{\circ }$
Hence $a={105}^{\circ },b={75}^{\circ }$