Question

1. choose all answers that describe the polygon klmn if kl = lm = mn = nk, m∠k = 81°, m∠l = 99°, m∠m = 81°, and m∠n = 99°.

□ parallelogram □ quadrilateral □ rectangle
□ rhombus □ square

Explanation:

Step1: Check the definition of a quadrilateral

A quadrilateral is a four - sided polygon. Since \(KLMN\) has four sides (\(KL\), \(LM\), \(MN\), \(NK\)), it is a quadrilateral.

Step2: Check the definition of a parallelogram

In a parallelogram, opposite angles are equal. Here, \(\angle K=\angle M = 81^{\circ}\) and \(\angle L=\angle N=99^{\circ}\). Also, in a parallelogram, opposite sides are equal (\(KL = LM=MN = NK\) is given). So, \(KLMN\) is a parallelogram.

Step3: Check the definition of a rhombus

A rhombus is a parallelogram with all sides equal. Given \(KL = LM=MN = NK\), and since it is already a parallelogram (opposite angles are equal), \(KLMN\) is a rhombus.

Step4: Check the definitions of a rectangle and a square

A rectangle has four right angles (\(90^{\circ}\)). Since \(\angle K = 81^{\circ}
eq90^{\circ}\) and \(\angle L=99^{\circ}
eq90^{\circ}\), it is not a rectangle. A square is a special case of a rectangle (all angles \(90^{\circ}\)) and a rhombus. Since it is not a rectangle, it is not a square.

Answer:

• Quadrilateral
• Parallelogram
• Rhombus