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

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Solution

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

We know that, if two angles are complementary, then their sum is $90^{o}$ .

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

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

$⟹$ $3 x - 15^{o} = 90^{o}$

$⟹$ $3 x = 15^{o} + 90^{o}$

$⟹$ $3 x = 105^{o}$

$⟹$ $x = \frac{105^{o}}{3}$

$⟹$ $x = 35^{o}$ .

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

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