Chapter 12, Problem 11STP

To determine

To determine the value of $x$ in the given figure.

Answer to Problem 11STP

  $31$

Explanation of Solution

Given:

  

In the given figure, $c\parallel d$ .

Concept used:

If a transversal crosses any two given parallel lines, then the corresponding angles formed have equal measure.

Calculation:

In the given figure, the two parallel lines $c$ and $d$ are intersected by a transversal.

So, the angles formed by the first line with the transversal have equal corresponding angles formed by the second line with the transversal.

  $\Rightarrow 4x+11=135$

  $\Rightarrow 4x=135-11$

[Subtracting $11$ on both sides]

  $\begin{array}{l}\Rightarrow 4x=124\\ \Rightarrow x=\frac{124}{4}\\ \Rightarrow x=31\end{array}$

Conclusion:

Therefore, the value of $x$ is $31$ .