Q.Two angles of a triangle are $\dfrac{5\pi}{9}^{c}$ and $\dfrac{5\pi}{18}^{c}$. Find the degree and radian measure of the third angle.

Step 1: Convert each given angle to degree.

$\frac{5\pi}{9}\times\frac{180}{\pi} = 5\times20 = 100°$.

$\frac{5\pi}{18}\times\frac{180}{\pi} = 5\times10 = 50°$.

Step 2: Third angle $= 180° - 100° - 50° = 30°$. …

Convert both given radian angles to degree, subtract their sum from 180°, then …

• Subtracting the two given angles from 180° while one is still in radian.
• Simplification slips converting 5π/9 and 5π/18 to degree. …