Question

in $△ABC,m\angle A={\frac{2\pi }{3}}^c$ and $m\angle B={45}^o$ Find $m\angle C$ in both system.

Answer 1

$M\angle A={\left(\frac{2\pi }{3}\right)}^C={(\frac{2}{3}\times 180)}^o={120}^o$

$\therefore M\angle B={45}^o$

$\therefore M\angle C={180}^o-{45}^o-{120}^o$

$\therefore M\angle C={15}^o$

$\therefore M\angle C={(\frac{\pi }{180}\times 15)}^C={\left(\frac{\pi }{12}\right)}^C$

$M\angle C={15}^o={\left(\frac{\pi }{12}\right)}^C$