Question

One of the angles forming a linear pair is a right angle. What can you say about its other angle?

Answer 1

Hint: Here we have been given that there are two angles which form a linear pair and the value of one of the angles is given. We have to find the value of another angle. Firstly we will write down the definition of linear pair then we will let the value of two angles and substitute one value which is given. Finally by using the definition of linear pair we will find the value of another angle and get our desired answer.

Complete step-by-step solution:
We have to find the value of the second angle of a linear pair when one angle is right angle.
As we know that two angles are said to be a linear pair if they are adjacent angles that means their sum is equal to ${{180}^{\circ }}$ .
Let the two angles that form a linear pair be $x$ and $y$ .
From the definition there sum should be equal to ${{180}^{\circ }}$ so,
$x+y={{180}^{\circ }}$…..$\left( 1 \right)$
As it is given that one angle is right-angle which means its value is ${{90}^{\circ }}$ so substitute $x={{90}^{\circ }}$ in equation (1) as follows,
${{90}^{\circ }}+y={{180}^{\circ }}$
On solving we get,
$\Rightarrow y={{180}^{\circ }}-{{90}^{\circ }}$
$\Rightarrow y={{90}^{\circ }}$
So we got the value of another angle as ${{90}^{\circ }}$ .
We know ${{90}^{\circ }}$ is equal to right-angle.
Hence the other angle of a linear pair of angles when one angle is right-angle is right-angle.

Note: Linear pair is angle on a straight line or we can say angles whose sum is ${{180}^{\circ }}$ . The two lines should intersect each other at a single point so that a linear pair of angles are formed. Adjacent angles are those which are formed when two angles have a common vertex and common side but they don’t overlap.