Question

In figure, if $a$ is grater than $b$ by one third af a right angle. Find the values of $a$ and $b$.

Answer 1

$a={105}^{\circ }b={75}^{\circ }$
From the figure, $\angle AOC$ and $\angle BOC$ are forming linear pair
$\Rightarrow \angle AOC+\angle BOC={180}^{\circ }$ $\Rightarrow a+b={180}^{\circ }\dots \left(1\right)$
According to the question,
$a=b+\frac{1}{3}\times {90}^{\circ }=b+30°$
$a-b={30}^{\circ }\dots \left(2\right)$
On adding equations $\left(1\right)$ and $\left(2\right)$, we get
$a+b+a-b={180}^{\circ }+{30}^{\circ }$ $2a={210}^{\circ }$
$a=\frac{{210}^{\circ }}{2}={105}^{\circ }$
$\therefore {105}^{\circ }+b={180}^{\circ }\Rightarrow b={180}^{\circ }-{105}^{\circ }={75}^{\circ }$
Hence, the value of $a={105}^{\circ }$ and $b={75}^{\circ }$.