Question

Select all true statements if n || m.

Parallel lines M and N cut by two transversals, A B and B C. Along line M, three angles are labeled 2, 3, and 4, which together form a straight angle. Transversal A B forms two angles below line N, one labeled 20 degrees and the other labeled A. Together, these angles form a straight angle. Transversal B C forms two angles below line N, one labeled C and the other labeled 60 degrees. Together, these angles form a straight angle. Angle 1 is vertical to the 60-degree angle and is an alternate interior angle to angle 4. Together, angles 1, 3, and an unlabeled angle that is vertical to the 20-degree angle form a triangle between the two parallel lines.
A. m∠2 = 60°
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
D. m∠2 + m∠3 = 80°
E. m∠2 = 20°

Answer 1

Hi, the correct answer is A) m∠2 = 60°.

let me put it in this way.

Explanation:

Since parallel lines M and N are cut by transversals A B and B C, corresponding angles are formed. Corresponding angles are pairs of angles that are formed by intersecting lines and are on opposite sides of the transversal. In this case, angles 2 and C are corresponding angles, as are angles 3 and A.

We know that angles 2 and C form a straight angle along line M, and angles C and 60 degrees form a straight angle along line N. Since corresponding angles are congruent (have the same measure), this means that angle 2 must have the same measure as the 60-degree angle