Question

Two angles form a linear pair. If the measure of the angles is represented by $3x + 5$ and $x + 15$, then what is the value of x?

Answer 1

Hint: It should be clear that here the linear pair means the sum of two angles is ${180^ \circ }$. Here we know the values of two angles. So, we just have to make the equation according to the given property and then we have to find the value of x.

Complete step-by-step answer:

In the above question, it is given that the angles form a linear pair. It means that the sum of two angles is ${180^ \circ }$.
Therefore, we have to find the value of x using the above property and by forming an equation which helps us in finding the value of x.
According to the question,
$ \Rightarrow \left( {3x + 5} \right) + \left( {x + 15} \right) = {180^ \circ }$
Now, adding the constant term with the constant term and variable term with the variable term.
$ \Rightarrow 4x + 20 = {180^ \circ }$
Now transposing ${20^ \circ }$ to the right hand side.
$ \Rightarrow 4x = {180^ \circ } - {20^ \circ }$
After subtraction in RHS, we get
$ \Rightarrow 4x = {160^ \circ }$
Now, divide both sides by $4$.
$ \Rightarrow x = {40^ \circ }$
Therefore, the value of x is ${40^ \circ }$.
So, the correct answer is “${40^ \circ }$”.

Note: Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to ${180^ \circ }$. Such angles are also known as supplementary angles. The adjacent angles are the angles which have a common vertex. Hence, here as well the linear angles have a common vertex. Also, there will be a common arm which represents both the angles. A real-life example of a linear pair is a ladder which is placed against a wall, forming linear angles at the ground.