Chapter 5.3, Problem 3PSA

To determine

To Find: The values of remaining angles.

Answer to Problem 3PSA

  $m\angle 1=30°,m\angle 2=150°,m\angle 3=150°,m\angle 4=150°,m\angle 5=30°,m\angle 6=150°,m\angle 7=30°$

Explanation of Solution

Given:

  

  $a\parallel b$

Concept Used:

When two parallel lines are intersected by a transversal corresponding angles are equal.

Alternate interior angles are equal.

Calculation:

  

  $\begin{array}{l}\text{Since, when two parallel lines are intersected by a transversal corresponding angles are equal}\text{.}\\ \Rightarrow m\angle 1=30°\\ \Rightarrow m\angle 7=30°\\ \Rightarrow m\angle 5=m\angle 1=30°\\ \text{Also, sum of linear of angles is }180°\\ \Rightarrow \angle 1+\angle 2=180°\\ \Rightarrow 30°+\angle 2=180°\\ \Rightarrow \angle 2=150°\\ \Rightarrow m\angle 2=150°\\ \because \angle 6=\angle 2\left(\text{Corresponding angles}\right)\\ \Rightarrow m\angle 6=150°\\ \because \angle 6=\angle 3\left(\text{Alternate interior angles}\right)\\ \Rightarrow m\angle 3=150°\end{array}$