Mathematics

An angle is $$\dfrac{4}{5}$$ of its supplement. What is its magnitude?


SOLUTION
We have,
angle $$\dfrac {4}{5}$$
Let the angle be $$x$$
there for the compliment will be $$\left (90-\dfrac {4}{5}x\right)$$
$$x=\dfrac {4}{5}(90-x)$$
$$x=72-\dfrac {4}{5}x$$
$$x+\dfrac {4}{5}x=72$$
$$\dfrac {5x+4x}{5}=72$$
$$x=72\times \dfrac {5}{9}$$
$$x=40$$
the angle $$40^o$$ and its compliment is $$90-40=50^o$$
Hence this is the answer.
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