Question

Find the value of $x$?

Answer 1

Hint: In this question we have been given with a set of lines which make specific angles after intersection. We are given two parallel lines and a transversal line which intersects the parallel lines. We will solve this question by first giving names to all the angles in the given diagram. We will then use the property vertical opposite angles, supplementary angles and then again vertical opposite angles to get the value of $x$.

Complete step by step answer:
We can see from the diagram that the transversal line after intersection makes a total of $8$ angles. On naming the angles, we get:

Now from the diagram we can see that the measurement of angle $\angle c$ is ${{118}^{\circ }}$.
Since angle $\angle c$ and $\angle b$ are a pair of vertical opposite angles, we get the measurement of angle $\angle b$ as ${{118}^{\circ }}$.
Now from the diagram we can see that angles $\angle b$ and $\angle e$ are a pair of interior angles of the same side of the transversal.
We know that interior angles on the same sides of the transversal are supplementary angles therefore the sum of both the angles will be ${{180}^{\circ }}$.
Therefore, we have the value of angle $\angle e$ as:
$\Rightarrow \angle e={{180}^{\circ }}-\angle b$
On substituting the value of $\angle b$, we get:
$\Rightarrow \angle e={{180}^{\circ }}-{{118}^{\circ }}$
On simplifying, we get:
$\Rightarrow \angle e={{62}^{\circ }}$
Now we can see from the diagram that $\angle e$ and $\angle h$ are a pair of vertical opposite angles, therefore we have the value of $\angle h={{62}^{\circ }}$, which is the value of $x$ therefore, we can write:
$x={{62}^{\circ }}$, which is the required solution.

Note: It is to be remembered that whenever doing a question with parallel lines and its transversal, the various properties should be remembered such as the interior angles, the exterior angles, vertically opposite angles, corresponding angles, interior alternate angles, exterior alternate angles and the interior angles on the same side of the transversal.