Mathematics

Find the value of $$x$$ for which the angles $${(2x-5)}^{o}$$ and $${(x-10)}^{o}$$ are the complementary angles.


SOLUTION
It is given that $${(2x-5)}^{o}$$ and $${(x-10)}^{o}$$ are the complementary angles

So we can write it as

$${(2x-5)}^{o}+{(x-10)}^{o}={90}^{o}$$

$$2x-{5}^{o}+x-{10}^{o}={90}^{o}$$

On further calculation

$$3x-{15}^{o}={90}^{o}$$

So we get

$$3x={105}^{o}$$

By division

$$x=\dfrac{105}{3}$$

$$x={35}^{o}$$

Therefore, the value of $$x$$ for which the angles $${(2x-5)}^{o}$$ and $${(x-10)}^{o}$$ are the complementary angles is $${35}^{o}$$
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