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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 =2:3:4
let 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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