Chapter 12.2, Problem 21E

To determine

TO-DETERMINE: How $m\angle 2$ and $m\angle 3$ are related and illustrate the situation.

Answer to Problem 21E

  $\angle 2$ and $\angle 3$ are corresponding angles and $m\angle 2=m\angle 3$

Explanation of Solution

Given information : A transversal intersect two parallel lines, forming alternate interior angles $\angle 1$ and $\angle 2$ , vertical angles $\angle 1$ and $\angle 3$

Concept used : If transversal line intersect two parallel line, the angles occupy corresponding position are called corresponding angles and Corresponding angles are equal.

It is evident that $\angle 2$ and $\angle 3$ occupy the corresponding position. So, $\angle 2$ and $\angle 3$ are corresponding angles. Hence, $m\angle 2=m\angle 3$