Answer:
r and s cannot be parallel
Step-by-step explanation:
If a line intersects two parallel lines, then some special angles are formed between the parallel lines
- Alternate angles, they are equal in measures (corners of Z)
- Corresponding angles, they are equal in measures (corners of F on inside and the other outside)
- Interior angles, they measures add up to 180° (corners of U)
From the given figure
∵ Line r and line s intersected by line m
∵ m∠1 = 111°
∴ The angle adjacent ∠1 must be 180 - 111 = 69° ⇒ linear pairs
∵ The angle of measure 69° and angle 5 are in the corresponding
position
∴ m∠5 must be equal 69°
∵ m∠5 = 59° from the given
→ That means the lines cannot be parallel because the angles
in the corresponding position are not equal in measures.
∴ Lines r and s can not be parallel
