Short Answer 
The problem involves parallel lines m and n, where angles m∠1 = 50° and m∠2 = 42° are given. Using the triangle sum theorem, we find m∠3 = 88°, and since m∠3 ≅ m∠4, we determine m∠4 = 88°. Finally, applying the linear pair postulate, we find m∠5 = 92°.
Identify Given Angles and Theorems
Start by analyzing the given information. We know that lines m and n are parallel (m ∥ n), along with the measurements of angles: m∠1 = 50° and m∠2 = 42°. According to the triangle sum theorem, the angles of a triangle add up to 180°, which helps us determine that m∠3 = 88°.
Apply Corresponding Angles and Angle Congruence
Next, we utilize the property of corresponding angles on parallel lines: ∠3 ≅ ∠4. Since corresponding angles formed by two parallel lines and a transversal are congruent, it follows that m∠3 = m∠4. By substitution, this leads us to m∠4 = 88°.
Find the Measurement of Angle 5
Finally, we examine angles ∠4 and ∠5 which create a linear pair. By the linear pair postulate, we know m∠4 + m∠5 = 180°. Substituting the known value, we get 88° + m∠5 = 180°. Solving this equation using the subtraction property gives us m∠5 = 92°.