# Ex.5.2 Q6 Lines and Angles - NCERT Maths Class 7

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## Question

In the given figures below, decide whether $$l$$  is parallel to $$m.$$

## Text Solution

(i) Reasoning:

Let’s visually model this problem. There is one operation that can be done check whether interior angles are supplementary or not. According to this model, the result sum of $$126^\circ + 44^\circ$$ is $$170^\circ.$$ Now, it’s a matter of finding $$l$$ is parallel to $$m$$ or not

Steps:

(i) $$126^\circ + 44^\circ = 170^\circ$$

As the sum of interior angles on the same side of transversal $$n$$ is not $$180^\circ.$$

Therefore, $$l$$ is not parallel to $$m.$$

(ii) Reasoning:

Let’s visually model this problem. There are two operations that can be done in a sequence. First find the value of $$x$$ and then check it is equal to its corresponding angle or not. According to this model, the resultant value of $$x$$ is not equal to its corresponding angle. Now, it’s a matter of finding $$l$$ is parallel to $$m$$ or not

Steps:

$$\angle x + 75^\circ = 180^\circ$$ (Linear pair)

$$\angle x = 180^\circ - 75^\circ$$

$$\angle x = 105^\circ$$

For $$l$$ and $$m$$ to be parallel measure of their corresponding angles should be equal but here the measure of $$\angle x$$ is $$105^\circ$$ and its corresponding angle is $$75^\circ.$$

Therefore, the lines $$l$$ and $$m$$ are not parallel.

(iii) Reasoning:

Let’s visually model this problem. There are two operations that can be done in a sequence. First find the value of $$x$$ and then check it is equal to its corresponding angle or not. According to this model, the resultant value of $$x$$ is not equal to its corresponding angle. Now, it’s a matter of finding $$l$$ is parallel to $$m$$ or not

Steps:

$$\angle y=57^\circ$$ (Vertically opposite angles)

$$\angle x + 123^\circ = 180^\circ$$ (Linear pair)

$$\angle x = 180^\circ - 123^\circ$$

$$\angle x = 57^\circ$$

Here, the measure of corresponding angles are equal i.e $$57^\circ.$$

Therefore, lines l and m are parallel to each other.

(iv) Reasoning:

Let’s visually model this problem. There are two operations that can be done in a sequence. First find the value of $$x$$ by using linear pairand then check it is equal to its corresponding angle or not. According to this model, the resultant value of $$x$$ is not equal to its corresponding angle. Now, it’s a matter of finding $$l$$ is parallel to $$m$$ or not

Steps:

$$\angle x + 98^\circ = 180^\circ$$ (Linear pair)

$$\angle x = 180^\circ - 98^\circ$$

$$\angle x = 82^\circ$$

For $$l$$ and $$m$$ to be parallel measure of their corresponding angles should be equal but here the measure of corresponding angles are $$82^\circ$$ and $$72^\circ$$ whichn are not equal.

Therefore, $$l$$ and $$m$$ are not parallel to each other.

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