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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