Question

21a. 21b. one the diagram list one pair of each: choose all correct responses!
a) alternate interior angles
□ m∠4 and m∠5 □ m∠2 and m∠8
□ m∠2 and m∠6 □ m∠1 and m∠7
□ m∠3 and m∠6 □ m∠4 and m∠7
b) alternate exterior angles
□ m∠4 and m∠7 □ m∠2 and m∠8
□ m∠1 and m∠7 □ m∠3 and m∠6
□ m∠2 and m∠6 □ m∠4 and m∠5

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.

Step2: Check each pair for alternate interior angles

• For \(m\angle4\) and \(m\angle5\): They are on opposite sides of the transversal and between the two parallel lines (interior), so they are alternate interior angles.
• For \(m\angle3\) and \(m\angle6\): They are on opposite sides of the transversal and between the two parallel lines (interior), so they are alternate interior angles.

Step3: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent exterior angles that lie on opposite sides of the transversal.

Step4: Check each pair for alternate exterior angles

• For \(m\angle2\) and \(m\angle8\): They are on opposite sides of the transversal and outside the two parallel lines (exterior), so they are alternate exterior angles.
• For \(m\angle1\) and \(m\angle7\): They are on opposite sides of the transversal and outside the two parallel lines (exterior), so they are alternate exterior angles.

Answer:

a) Alternate interior angles: \(m\angle4\) and \(m\angle5\), \(m\angle3\) and \(m\angle6\)
b) Alternate exterior angles: \(m\angle2\) and \(m\angle8\), \(m\angle1\) and \(m\angle7\)