Question

If the supplement of an angle is $130{}^\circ $ then find its complement.

Answer 1

Hint: First we will assume that the angle be $x{}^\circ $. Then by using the definition of supplementary angles that the sum of supplementary angles is $180{}^\circ $, we will find the measure of angle. Then by using the definition of complementary angles we will get the desired answer.

Complete step by step answer:
We have been given that the supplement of an angle is $130{}^\circ $.
We have to find the complement of that angle.
Let us first consider the angle to be $x{}^\circ $.
Now, we know that the sum of two supplementary angles will be $180{}^\circ $.
So we will get
$\Rightarrow x{}^\circ +130{}^\circ =180{}^\circ $
Now, simplifying the above obtained equation we will get
\[\begin{align}
  & \Rightarrow x{}^\circ =180{}^\circ -130{}^\circ \\
 & \Rightarrow x{}^\circ =50{}^\circ \\
\end{align}\]
Now, we get the measure of an angle as \[50{}^\circ \].
Now, we know that if two angles are complementary to each other then their sum will be $90{}^\circ $.
To find the complementary angle of any particular angle we subtract the angle from the measure of the right angle.
So the complement of an angle measures \[50{}^\circ \] will be
\[\begin{align}
  & \Rightarrow 90{}^\circ -50{}^\circ \\
 & \Rightarrow 40{}^\circ \\
\end{align}\]
Hence we get the complement of an angle as \[40{}^\circ \].

Note: In mathematics the angles formed on the straight line are called straight angles and measure $180{}^\circ $. Thus two angles are called supplementary to each other when added should be equal to a straight angle. Similarly complementary angles when added should be equal to right angles. The value of an angle may be positive or negative.