Question

If $x$ is greater than $y$ by one-third of a right angle. Find $x$ and $y$

Answer 1

Solve for $x$ and $y$

Now according to the given condition

$x=y+\frac{{90}^{\circ }}{3}$

$x=y+{30}^{\circ }$ …..$\left(1\right)$

And,

$x+y={180}^{\circ }$ …..$\left(2\right)$
Now solve equation $\left(1\right)$ and $\left(2\right)$
$\begin{array}{rcl}2x& =& {210}^{\circ }\\ x& =& \frac{{210}^{\circ }}{2}\\ x& =& {105}^{\circ }\\ & & \mathrm{Also},\\ x–y& =& {30}^{\circ }\\ y& =& x–{30}^{\circ }\\ & =& {105}^{\circ }–{30}^{\circ }\\ y& =& {75}^{\circ }\end{array}$

Hence the value of $x$ and $y$ is ${105}^{\circ }$ and ${75}^{\circ }$ respectively.