Exercise 23 Page 508

First, let's label some of the angles in the diagram. We are told that that m∠ 1=25^(∘). Using this, and the markings shown in the diagram, we can identify a few pairs of complementary angles.

The path of the ball can be viewed as a transversal cutting the two vertical lines. Since the vertical lines are parallel, we can identify a pair of alternate interior angles, which we know are congruent by the Alternative Interior Angles Theorem.

Examining the figure, we can see that something is very, very incorrect. When the cue ball is hit, the angles created by the path of the ball, with the vertical line along the point of impact, should be congruent. Two examples of this are shown below.

However, when m∠ 1 =25^(∘), are not congruent. If our friend had claimed that m∠ 1 =65^(∘), he would have been correct.