Question

How do you find the complement and supplement of $18^\circ $?

Answer 1

Hint: Always remember that the sum of two complementary angles is always ninety degrees. The sum of two angles in supplementary is always one-eighty degree. Then will place it in the given expression and will simplify for the required solution.

Complete step by step answer:
Given that Angle $18^\circ $
Complement of the above angle can be given by -
$x + 18^\circ = 90^\circ $
Make the required value of “x” the subject and move other terms on the opposite side. When you move any term from one side to another then the sign of the term also changes. Positive terms becomes negative.
 $ \Rightarrow x = 90^\circ - 18^\circ $
Simplify the above expression –
$ \Rightarrow x = 72^\circ $ …. (A)
Now, the supplementary angle can be given by –
$x + 18^\circ = 180^\circ $
Make the required value of “x” the subject and move other terms on the opposite side. When you move any term from one side to another then the sign of the term also changes. Positive term become negative.
 $ \Rightarrow x = 180^\circ - 18^\circ $
Simplify the above expression –
$ \Rightarrow x = 162^\circ $ …. (B)
The equations (A) and (B) are the required solutions.

Note: Always remember the difference between the complementary and supplementary angles. Be careful about the sign convention and while simplifying. Always remember that the sign of the term changes when you move any term from one side to another.