Mathematics

Find the measure of an angle which is $${ 30 }^{ \circ  }$$ less than its supplement.


SOLUTION
Consider the required angle as $${x}^{o}$$

We know that the complement can be written as $${180}^{o}-{x}^{o}$$

To find the measure of an angle is equal to its complement 

We get

$${x}^{o}=[{180}^{o}-{x}^{o}]+{30}^{o}$$

We can also write it as

$$x+x=90+36$$

So we get

$$2x=150$$

By division we get

$$x=\dfrac{150}{2}$$

$${x}^{o}={75}^{o}$$

Therefore the measure of an angle which is $${30}^{o}$$ more than its complement is $${75}^{o}$$
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