Question

In the figure, lines I and mare parallel lines cut by transversal p.

Andrea said that if m 2 2 = 40° then m 3 must also be equal to 40°. Which justifies Andrea's statement?
A
Alternate interior angles are congruent.
B. Alternate exterior angles are congruent.
C. Corresponding angles are congruent,
D. Consecutive interior angles are supplementary

Answer 1

The statement which justifies Andrea's statement is "Corresponding angles are congruent" ⇒ C

Explanation:

If two parallel lines intersected by a line, then there are some pair of angles are formed

• Corresponding angles that are congruent

• Alternate interior angles that are congruent

• Alternate exterior angles that are congruent

• Consecutive interior angles that are supplementary

In the given figure

∵ Lines l and m are parallel

∵ They are cut by transversal p

∵ ∠2 and ∠3 are in the corresponding position

→ By using the 1st rule above

∵ Corresponding angles are congruent

∴ ∠2 ≅ ∠3

∴ m∠3 = m∠2

∵ m∠2 = 40°

∴ m∠3 = 40°

The statement which justifies Andrea's statement is "Corresponding angles are congruent"