Question

if angle 4 is 42° and lines m and n are parallel, give a reason why angle 5 is also 42°. (1 point) angle 4 and angle 5 are interior angles, so their measures must be the same. angle 4 and angle 5 are alternate interior angles, so their measures must be the same. angle 4 and angle 5 are corresponding angles, so their measures are congruent. angle 4 and angle 5 are vertical angles, so their measures are congruent.

Explanation:

• Interior angles: There is no such specific property for just "interior angles" to be equal.
• Alternate interior angles: When two parallel lines are cut by a transversal, alternate interior angles are congruent. Angle 4 and angle 5 fit this definition.
• Corresponding angles: Corresponding angles have a different positional relationship (e.g., in the same relative position at each intersection). Angle 4 and 5 do not match this.
• Vertical angles: Vertical angles are formed by two intersecting lines. Here, the relationship is due to parallel lines and a transversal, not just two intersecting lines.

Answer:

Angle 4 and angle 5 are alternate interior angles, so their measures must be the same.