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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Subjective Medium Published on 09th 09, 2020
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