Question

If the radian measures of two angles of a triangle are $\frac{3\pi }{5},\frac{4\pi }{15}$. Find the radian measure and the degree measure of the third angle.

Answer 1

In a triangle ,sum of radian measures of three measures of three angles will be $\pi$

Given two angles in radians are $\frac{3\pi }{5},\frac{4\pi }{15}$

third angle will be $\pi -\frac{3\pi }{5}-\frac{4\pi }{15}=\frac{2\pi }{15}$

degree measure of third angle will be $\frac{2\pi }{15}\times \frac{{180}^{\circ }}{\pi }={24}^{\circ }$