When two parallel lines are cut by a transversal, same-side interior angles are

When two parallel lines are cut by a transversal, same-side interior angles are

• A. Congruent
• B. Supplementary
• C. Complementary
• D. Vertical

Answer: (B)

When two parallel lines are cut by a transversal, interior angles that lie between the lines on the same side of the transversal add up to 180 degrees. These are called same-side (or consecutive) interior angles, and they are supplementary. Think of one interior angle at the first intersection on that side. The angle next to it along the straight line at that intersection forms a linear pair, so they sum to 180 degrees. The exterior angle adjacent to the interior angle is congruent to the interior angle on the second intersection on the same side because alternate interior angles are equal when the lines are parallel. Putting those facts together, the two interior angles on the same side must sum to 180 degrees. That’s why same-side interior angles are supplementary. The other options don’t fit: congruent would describe alternate interior or corresponding angles, complementary would sum to 90, and vertical angles are opposite angles at a single intersection.

When two parallel lines are cut by a transversal, interior angles that lie between the lines on the same side of the transversal add up to 180 degrees. These are called same-side (or consecutive) interior angles, and they are supplementary.

Think of one interior angle at the first intersection on that side. The angle next to it along the straight line at that intersection forms a linear pair, so they sum to 180 degrees. The exterior angle adjacent to the interior angle is congruent to the interior angle on the second intersection on the same side because alternate interior angles are equal when the lines are parallel. Putting those facts together, the two interior angles on the same side must sum to 180 degrees.

That’s why same-side interior angles are supplementary. The other options don’t fit: congruent would describe alternate interior or corresponding angles, complementary would sum to 90, and vertical angles are opposite angles at a single intersection.