Question

17 select all true statements about the following parallelogram: parallelogram lkmj with angle at j being 98° and angle at l being? a ∠k ≅ ∠l b ∠j ≅ ∠l c ∠k = 82° d ∠k and ∠j are supplementary e ∠m ≅ ∠j

Explanation:

Step1: Properties of parallelogram

In a parallelogram \(KLMJ\), \(KL\parallel MJ\) and \(LM\parallel KJ\). Opposite angles of a parallelogram are equal. So \(\angle K=\angle M\) and \(\angle L = \angle J\). Also, consecutive angles of a parallelogram are supplementary. So \(\angle K+\angle J = 180^{\circ}\), \(\angle L+\angle M=180^{\circ}\), \(\angle K+\angle L = 180^{\circ}\), \(\angle M+\angle J=180^{\circ}\)

Step2: Analyze each option

• Option A:

Since \(\angle K+\angle L = 180^{\circ}\) (consecutive angles of a parallelogram), \(\angle K
ot\cong\angle L\) unless the parallelogram is a rectangle. So \(A\) is false.

• Option B:

Since \(\angle J+\angle L=180^{\circ}\) (consecutive angles of a parallelogram), \(\angle J
ot\cong\angle L\) unless the parallelogram is a rectangle. So \(B\) is false.

• Option C:

Since \(\angle K+\angle J = 180^{\circ}\) (consecutive angles of a parallelogram) and \(\angle J = 98^{\circ}\), then \(\angle K=180^{\circ}-\angle J=180 - 98=82^{\circ}\). So \(C\) is true.

• Option D:

Since \(\angle K+\angle J = 180^{\circ}\) (consecutive angles of a parallelogram), \(\angle K\) and \(\angle J\) are supplementary. So \(D\) is true.

• Option E:

Since \(\angle M=\angle K\) (opposite angles of a parallelogram) and \(\angle K = 82^{\circ}\), \(\angle M = 82^{\circ}\), \(\angle J=98^{\circ}\). So \(\angle M
ot\cong\angle J\). So \(E\) is false.

Answer:

C. \(\angle K = 82^{\circ}\), D. \(\angle K\) and \(\angle J\) are supplementary