Question

Find the angle which is supplementary of itself?

Answer 1

Hint: Let us assume the angle be x and this angle is supplementary to itself so the supplementary angle is also x. Now, we know that when two angles are supplementary meaning the sum of two angles is ${{180}^{\circ }}$ so sum of x and its supplementary angle x is equal to ${{180}^{\circ }}$. Now, solve this equation and get the value of x which is the angle required.

Complete step-by-step answer:
We are asked to find the angle which is supplementary to itself so let us assume that angle is x.
Now, the supplementary angle of this angle is equal to itself meaning the angle supplement to x is x itself.
In the below figure, we have drawn the equal angles of measure x.

We know that the sum of supplementary angles is equal to ${{180}^{\circ }}$ so adding x with x and then equate it to ${{180}^{\circ }}$.
$\begin{align}
  & x+x={{180}^{\circ }} \\
 & \Rightarrow 2x={{180}^{\circ }} \\
\end{align}$
Dividing 2 on both the sides of the above equation we get,
$\begin{align}
  & x=\dfrac{{{180}^{\circ }}}{2} \\
 & \Rightarrow x={{90}^{\circ }} \\
\end{align}$
From the above solution, we have got the value of x as ${{90}^{\circ }}$ which is the angle that we are asked for.
Hence, ${{90}^{\circ }}$ is the angle which is supplementary to itself.

Note: You can verify the angle that you are getting in the above solution as follows.
It is given that the angle is supplementary of itself meaning the angle and its supplementary are equal. The angle that we have obtained above is ${{90}^{\circ }}$ this angle is supplementary to the same angle that is ${{90}^{\circ }}$
Let us assume that the other supplementary angle is y so summation of y and ${{90}^{\circ }}$ is equal to ${{180}^{\circ }}$.
${{90}^{\circ }}+y={{180}^{\circ }}$
Subtracting ${{90}^{\circ }}$ on both the sides of the above equation we get,
$\begin{align}
  & y={{180}^{\circ }}-{{90}^{\circ }} \\
 & \Rightarrow y={{90}^{\circ }} \\
\end{align}$
Hence, we have got the same angle that we have solved above. Hence, we have verified that the angle that we have solved above is correct.