Each angle pair and the transversal that connects each of them should be named as follows;
∠4 and ∠10: Consecutive interior angles. Transversal: Line k.
∠5 and ∠7: Corresponding. Transversal: Line j.
∠8 and ∠11: Alternate exterior angles. Transversal: Line m.
∠2 and ∠12: No relationship. Transversal: Line k.
∠2 and ∠13: Alternate interior angles. Transversal: Line l.
The consecutive interior angles theorem states that when two parallel lines are cut through by a transversal, the interior angles that are formed are congruent and each pair of the consecutive interior angles is supplementary.
By applying the consecutive interior angles theorem, we have the following supplementary angles:
m∠4 + m∠10 = 180° (Transversal line k)
By applying the corresponding angles theorem, we have the following congruent angles:
m∠5 ≅ m∠7 (Transversal line j)
By applying the alternate exterior angles theorem, we have the following congruent angles:
m∠8 ≅ m∠11 (Transversal line m)
By applying the alternate interior angles theorem, we have the following congruent angles:
m∠2 ≅ m∠13 (Transversal line l)
Complete Question:
Name each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior angle, or no relationship. Identify the transversal that connects each angle pair.
∠4 and ∠10: _____ Transversal: ____
∠5 and ∠7: _____ Transversal: ____
∠8 and ∠11: _____ Transversal: ____
∠2 and ∠12: _____ Transversal: ____
∠2 and ∠13: _____ Transversal: ____