Exercise 56 Page 452

Let's begin by labeling the given angles, along with a third angle that will help us later.

Since ∠ 1 and ∠ 3 are vertical angles, they are congruent by the Vertical Angles Theorem. m∠ 1 = m∠ 3 Now, ∠ 2 and ∠ 3 are alternate exterior angles. For lines m and n to be parallel, this last pair of angles must be congruent according to the Alternate Exterior Angles Theorem. m∠ 2 = m∠ 3 Using that m∠ 1=m∠ 3, we can rewrite this equation. m∠ 2 = m∠ 1 Finally, we substitute the measures of the angles and solve the equation for x.