Question

two parallel lines, p and q, are cut by the transversal f as shown. suppose m∠1 = 65°. compare the statements below.

Explanation:

Step1: Find the relationship between ∠1 and ∠2

∠1 and ∠2 are supplementary angles (they form a linear pair).
$$m\angle1 + m\angle2=180^{\circ}$$

Step2: Calculate the measure of ∠2

Substitute \(m\angle1 = 65^{\circ}\) into the equation.
$$65^{\circ}+m\angle2 = 180^{\circ}$$
$$m\angle2=180^{\circ}- 65^{\circ}$$
$$m\angle2 = 115^{\circ}$$

Step3: Find the relationship between ∠1 and ∠3

∠1 and ∠3 are alternate interior angles. Since \(p\parallel q\), alternate interior angles are equal.
$$m\angle1=m\angle3$$
$$m\angle3 = 65^{\circ}$$

Answer:

\(m\angle2 = 115^{\circ}\), \(m\angle3 = 65^{\circ}\)