Question

Those angles are alternate exterior angles. If a pair of alternate exterior angles are congruent we can conclude that the lines l and m are parallel.

Answer 1

Question 1:

- The angles labeled 63 are equal because they are Exterior Alternate Angles and Exterior Alternate Angles are equal.

- Thus, we can conclude that lines l and m are parallel lines.

- The converse is Converse of Alternate Exterior Angles

Question 2:

- The two angles marked on the question are equal because they are Corresponding Angles.

- Thus, we can conclude that lines l and m are parallel lines.

- The converse is Convers of Corresponding Angles

Question 3:

- The angle supplementary to 132 is 48 on the same line. This newly found 48-degree angle is equal to the 48-degree angle given in the question because they are Exterior Alternate Angles

- Thus, lines l and m are parallel.

- The converse is Contrapositive of the Converse of Alternate Exterior Angles

Question 4:

- The two angles labeled 105 degrees are equal because they are Vertically Opposite Angles.

- This does NOT guarantee that the lines l and m are parallel

Question 5:

- The two angles given are equal because they are Interior Alternate Angles

- Thus, the lines l and m are parallel

- The converse is Converse of Interior Alternate Angles

Question 6:

- The two angles given do not add up to 180 degrees. Rather, they add up to 190 degrees.

- Thus, the lines l and m are NOT parallel