Q.One angle of a quadrilateral has measure $\dfrac{2\pi}{5}^{c}$ and the measures of other three angles are in the ratio 2:3:4. Find their measures in degree and radian.

Step 1: Convert the given angle: $\frac{2\pi}{5}\times\frac{180}{\pi}=2\times36=72°$.

Step 2: Remaining sum $= 360°-72°=288°$. Split in ratio $2:3:4$ (parts sum to $9$): $k=\frac{288°}{9}=32°$.

Step 3: The other three angles: $2k=64°$, $3k=96°$, $4k=128°$. …

Convert the given radian angle to degree, subtract from the quadrilateral's 360° total, then split the remainde …

• Splitting the full 360° in the ratio instead of the remaining 288° after removing the known angle. …