Exercise 34 Page 306

Let's write the given conditional statement by dividing it into hypothesis and conclusion. Hypothesis:& If one of the angles formed by two & intersecting lines is acute, Conclusion:& then the other three angles & formed are also acute. Now, let's make a diagram that illustrates this situation.

Let's suppose ∠ 1 is acute. Since ∠ 1 and ∠ 3 are vertical angles, then ∠ 3≅ ∠ 1. Thus, ∠ 3 is also acute.

On the other hand, since ∠ 1 and ∠ 2 are supplementary, we know that the sum of their measures equals 180. m∠ 1 + m∠ 2 = 180 Since m∠ 1< 90, in order to satisfy the equation above, it be that m∠ 2 > 90. Hence, ∠ 2 is obtuse. This tells us that the given statement is never true.

Note: Since ∠ 2≅ ∠ 4 are vertical angles, ∠ 4 is also obtuse. Thus, there are 2 acute angles and 2 obtuse angles.