Question

The sum of two angles is $5{\pi }^c$ and their difference is ${60}^{\circ }$ . Find the angles in degrees.

Answer 1

Let $x$ & $y$ be the two anfers

$x+y=5\pi .....\left(1\right)$

$x-y=\frac{\pi }{3}...........\left(2\right)$

$[{60}^o=\frac{\pi }{3}]$

Add $\left(1\right)$ & $\left(2\right)$

$2x=5\pi +\frac{\pi }{3}$

$2x=\frac{16\pi }{3}$

$x{\left(\frac{8\pi }{3}\right)}^2$

Converting ${\left(\frac{8\pi }{3}\right)}^2$ to degrees

$\pi$ radian $={180}^o$

$1$ radian $=\frac{180}{\pi }$ degrees

$\frac{3\pi }{3}$ radian $=\frac{180}{\pi }\times \frac{8\pi }{3}$

$x={480}^o$

$x+y=5\left(380\right)={900}^o$

$y=900-480={420}^o$

$\Rightarrow x={480}^o,y={420}^o$