Question

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

Solution

## Sum of all angles of quadrilateral = $$2\pi$$ratio of rest angles =2:3:4let it be ratio = $$x$$$$2x+3x+4x+\dfrac{2\pi}{5}=2\pi$$$$45x=8\pi$$$$x=\dfrac{8\pi}{45}$$rest of other angles are=$$\dfrac{16\pi}{45},\dfrac{24\pi}{45},\dfrac{32\pi}{45}$$Mathematics

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