# Ex.5.2 Q4 Lines and Angles - NCERT Maths Class 7

## Question

Find the value of \(x\) in each of the following figures if \(l || m.\)

## Text Solution

**(i) Reasoning:**

There are two operations done in sequence. First, find the corresponding angle to \(110^\circ\) i. e \(\angle y,\) then by using Linear pair find the value of \(\angle x.\)

According to this model, the result \(\angle x + \angle y = 180^\circ.\) Now, it’s a matter of finding value of \(\angle x.\)

**(i) Steps:**

Solve for \(x\)

Given \(l || m\) and \(t\) is transversal,

\[\begin{align}\angle y &= 110^\circ\text{(Corresponding angle)}\\ \angle x+\angle y &= 180^\circ\text{(Linear pair)}\\\angle x &= 180^\circ - 110^\circ\\\angle x &= 70^\circ\end{align}\]

**(ii) Reasoning:**

Let’s visually model this problem. There is one operation that can be done. Find the corresponding angle to \(x.\) According to this model, the resultant value of corresponding angle will be equal to \(x.\) Now, it’s a matter of finding measure of \(x.\)

**(ii) Steps:**

Solve for \(x\)

Given \(l || m\) and \(a || b,\)

\[\angle x = 100^\circ \text{(corresponding angle)}\]