Question

If AC and BD are parallel lines and angle 5 is decreased by 30 degrees, how must angle 2 be changed to keep the lines parallel?

A) Angle 2 must be decreased by 30 degrees.
B) Angle 2 must be increased by 30 degrees.
C) Angle 2 remains unchanged.
D) Angle 2 must be decreased by 60 degrees.

Answer 1

To maintain parallelism between lines AC and BD, if angle 5 is decreased by 30 degrees, angle 2 must also be decreased by 30 degrees.

Step-by-step explanation:

If AC and BD are parallel lines and angle 5 is decreased by 30 degrees, to keep the lines parallel, angle 2 must be changed in such a way that it maintains the overall angles that are required for parallel lines. In the geometry of parallel lines, the alternate interior angles, corresponding angles, and the consecutive interior angles are equal or supplementary depending on their position in relation to the parallel lines. Therefore, if angle 5 which corresponds with angle 2 is decreased by 30 degrees, angle 2 would also need to be decreased by 30 degrees to keep them supplementary (if they are on the same side of the transversal) or equal (if they are alternate interior angles).

The correct option is: A) Angle 2 must be decreased by 30 degrees.