Chapter 5.2, Problem 16PSA

To determine

To Find: The value of $x$ which satisfy the given condition.

Answer to Problem 16PSA

  $x=26$ , also $m\parallel n$

Explanation of Solution

Given:

  

Concept Used:

When two parallel lines are intersected by a transversal, following pairs of angles are congruent:

• Alternate Interior Angles
• Alternate Exterior Angles
• Corresponding Angles

Calculation:

  $\begin{array}{l}\text{Since, we know that when lines are intersecting each other Vertically opposite Angles are congruent}\text{.}\\ \Rightarrow \left(5x-20\right)°=\left(x+84\right)°\left(\text{Vertically opposite Angles}\right)\\ \Rightarrow 4x=104\\ \Rightarrow x=26\\ \therefore \left(x+84\right)°=\left(26+84\right)°=110°\\ \Rightarrow \left(x+84\right)°=110°\left(\text{Corresponding Angles}\right)\\ \text{Since, we know that when two parallel lines are intersected by a transversal,}\\ \text{pairs of Corresponding Angles are congruent}\text{.}\\ \Rightarrow m\parallel n\end{array}$