Chapter 5, Problem 25RP

To determine

To Find: The value of $x$

Answer to Problem 25RP

  $x=60$

Explanation of Solution

Given:

  

Concept Used:

When two parallel lines intersected by a transversal, then:

• Alternate interior angles are equal.
• Corresponding angles are equal.
• Angles on the same side of transversal are supplementary.

Calculation:

After drawing the parallel lines through the angles $x^{\circ }\text{and }{50}^{\circ }$ , we get

  

Since, when two parallel lines intersected by a transversal, then:

• Alternate interior angles are equal.
• Corresponding angles are equal.
• Angles on the same side of transversal are supplementary.

  $\begin{array}{l}{a}^{\circ }+{140}^{\circ }={180}^{\circ }\left(\text{Angles on the same side of transversal are supplementary}\text{.}\right)\\ \Rightarrow a=40\\ d=20\left(\text{Alternate interior angles are equal}\right)\\ \because c^{\circ }+d^{\circ }={50}^{\circ }\\ \Rightarrow c^{\circ }+{20}^{\circ }={50}^{\circ }\\ \Rightarrow c=30\\ \because b=c\left(\text{Alternate interior angles are equal}\right)\\ \Rightarrow b=30\\ \because x=a+b\\ \Rightarrow x=40+20\\ \therefore x=60\end{array}$

Conclusion:

  $x=60$