Question

Polygon KLMN is the image of polygon PQRS after a 180-degree rotation. Which angle of polygon KLMN is congruent to angle S?

a) angle K
b) angle L
c) angle M
d) angle N

Answer 1

Angle S of polygon PQRS will be congruent to angle K of polygon KLMN after a 180-degree rotation, since they occupy opposite positions in the rotated image.

Step-by-step explanation:

When a polygon undergoes a 180-degree rotation, each vertex of the polygon gets rotated to the position directly opposite of it. In the case of polygon PQRS being rotated to become polygon KLMN, each corresponding angle of PQRS will be congruent to the angle at the vertex directly opposite of it in KLMN. Therefore, if we are looking for the angle of polygon KLMN that is congruent to angle S of polygon PQRS, we need to look for the angle that is opposite of S after the rotation.

After the rotation, the vertices are mapped as follows:

• Point P maps to point N, so angle P corresponds to angle N.
• Point Q maps to point M, so angle Q corresponds to angle M.
• Point R maps to point L, so angle R corresponds to angle L.
• Point S maps to point K, so angle S corresponds to angle K.

Therefore, the answer is (a) angle K which is congruent to angle S after the 180-degree rotation.