Question

If the radian measures of two angles of a triangle are $\frac{5\pi }{9},\frac{5\pi }{18}$. Find the radian measure and the degree measure of the third angle.

Answer 1

In any triangle ,sum of angles in a triangle is $\pi$

Given two angles in radians are $\frac{5\pi }{9},\frac{5\pi }{18}$

Third angle in radians will be $\pi -\frac{5\pi }{9}-\frac{5\pi }{18}=\frac{3\pi }{18}=\frac{\pi }{6}$

$⟹$ third angle in degrees will be $\frac{\pi }{6}\times \frac{{180}^{\circ }}{\pi }={30}^{\circ }$