Solution
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