Chapter 12.2, Problem 1E

To determine

To identify:Two pairs of alternate interior angles.

Answer to Problem 1E

Both pairs of alternate angles are,

  $\angle 4\text{ and }\angle 5$ , $\angle 3\text{ and }\angle 6$ .

Explanation of Solution

Given information: Two lines anda transversal intersect both the lines.

Calculation:

Let $m\text{ and }n$ be the two lines and let $l$ be thetransversal intersecting both the lines.

Let 1, 2, 3, 4, 5, 6, 7, 8 be the number of angles formed after intersection of line $l$ .

Figure:

  

Since, alternate interior angles are equal,

Therefore,

  $\angle 4\text{ = }\angle 5$ and $\angle 3=\angle 6$

Thus, both pairs of alternate angles are,

  $\angle 4\text{ and }\angle 5$ , $\angle 3\text{ and }\angle 6$ .