Question

In the figure, find the value of x for which the lines l and m are parallel.

(a)$${136}^{\circ }$$
(b)$${44}^{\circ }$$
(c)$${46}^{\circ }$$
(d)$${134}^{\circ }$$

Answer 1

Hint: In the parallel lines use the concept of interior angles and apply the property that the sum of interior angles is $${180}^{\circ }$$, thus substitute the value and find the value of x.

Complete step-by-step answer:
In the question we are given a figure and we have to find the value of x.
The figure is,

It contains two straight lines l, m which are parallel to each other which is cut by a straight line n or a transversal at two points let it be named as A, B.
So, here angle of A is measured as x and angle of B is given as B. As we know that here angle A and angle B together known as co – interior angles or we can say that if two parallel lines are cut by transversal like l and m by line n then $$\mathrm{\angle }BAE$$ and $$\mathrm{\angle }ABF$$ cuts as co – interior angles that it’s sum is equal to $${180}^{\circ }$$ or 2 right angles.
So, according to that,
$$\mathrm{\angle }EAB+\mathrm{\angle }ABF={180}^{\circ }$$
As we are given that $$\mathrm{\angle }EAB$$ is ‘x’ and $$\mathrm{\angle }ABF={44}^{\circ }$$. So, on substituting we can write it as,
$$x+{44}^{\circ }={180}^{\circ }$$
Or, $$x={180}^{\circ }-{44}^{\circ }$$
So, the value of x is $${136}^{\circ }$$.
Hence, the correct option is (a).

Note: We can also use the concept of corresponding angles, that corresponding angles are equal. Hence, corresponding angles are $$\mathrm{\angle }DAE$$ and $$\mathrm{\angle }ABF$$ which are equal. After then apply angles in a straight line which sums up to $${180}^{\circ }$$.