Question

One angle of a quadrilateral has measure $\frac{2\pi }{5}$ and the measure of other three angles are in the ratio $2:3:4$.Find their measure in radians ?

Answer 1

Sum of all angles of quadrilateral = $2\pi$

ratio of rest angles =2:3:4

let it be ratio = $x$

$2x+3x+4x+\frac{2\pi }{5}=2\pi$

$45x=8\pi$

$x=\frac{8\pi }{45}$

rest of other angles are=$\frac{16\pi }{45},\frac{24\pi }{45},\frac{32\pi }{45}$