Question

In triangle ABC, m angle A=2π/3 radian
m angle B = 45°. Find m angle C in degree and radian measure.​

Answer 1

$Given ,\: In \: \triangle ABC , \\\angle A = \frac{2\pi }{3} ,\: \angle B = 45\degree= \frac{\pi}{4} ,\\\angle C = ?$

$\underline {\pink {( Angle \: Sum \: Property )}}$

$\angle A + \angle B + \angle C = \pi$

$\implies \frac{2\pi }{3} + \frac{\pi}{4} + \angle C = \pi$

$\implies \frac{8\pi + 3\pi }{12} +\angle C = \pi$

$\implies \frac{11\pi }{12} +\angle C = \pi$

$\implies \angle C = \pi - \frac{11\pi}{12}$

$\implies \angle C = \frac{12\pi - 11\pi}{12}$

$\implies \angle C = \frac{\pi}{12} \:--(1)$

$\implies \angle C = \frac{180\degree}{12}$

$\boxed { \pink { Since,\:\pi = 180\degree }}$

$\implies \angle C = 15\degree \: ---(2)$

Therefore.,

$\red { \angle C } \green { = \frac{\pi}{12} = 15\degree }$

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