Question

parallelogram jklm is shown.

if the measure of angle m is 123 and parallelogram jklm was rotated 180 clockwise about the origin to create parallelogram jklm, what would the measure of angle l be?

a. 69
b. 123
c. 47
d. 57

Explanation:

Step1: Properties of parallelogram

In a parallelogram, consecutive angles are supplementary. So, \(\angle M+\angle L = 180^{\circ}\).

Step2: Solve for \(\angle L\)

Given \(\angle M = 123^{\circ}\), then \(\angle L=180^{\circ}-\angle M\). Substitute \(\angle M = 123^{\circ}\) into the formula: \(\angle L=180 - 123=57^{\circ}\). Also, rotation is a rigid transformation. Rigid transformations (like a \(180^{\circ}\) rotation) preserve the measures of angles.

Answer:

D. \(57^{\circ}\)