Question

what is the measure of angle l in parallelogram lmno?
20°
30°
40°
50°
(image shows parallelogram lmno with angle at n labeled 120° and angle at l labeled (3x - 20)°)

Explanation:

Step1: Use property of parallelogram

In a parallelogram, consecutive angles are supplementary. So, \(\angle M+\angle H = 180^{\circ}\). Given \(\angle H=60^{\circ}\), and \(\angle M=(3x - 20)^{\circ}\).

Step2: Solve for \(x\)

\((3x - 20)+60 = 180\)
\(3x+40 = 180\)
\(3x=180 - 40\)
\(3x = 140\) (This step seems wrong. Wait, no, in a parallelogram, opposite angles are equal. So \(\angle H=\angle L\) and \(\angle M=\angle O\). Also, \(\angle M+\angle H=180^{\circ}\) (adjacent angles). Wait, if we assume the problem is about adjacent angles. Wait, no, another property: in a parallelogram \(LMNO\), \(\angle H\) and \(\angle L\) are adjacent. Wait, no, actually, in parallelogram \(LMNO\), \(\angle M\) and \(\angle H\) are adjacent. So \(\angle M+\angle H = 180^{\circ}\). If \(\angle H = 60^{\circ}\), then \(\angle M=120^{\circ}\). But if the problem is just to find the measure of \(\angle L\). Wait, no, wait, in a parallelogram, opposite angles are equal. So \(\angle H=\angle L\). So if \(\angle H = 60^{\circ}\), then \(\angle L=60^{\circ}\)

Answer:

\(60^{\circ}\) (Assuming the options had \(60^{\circ}\) as one of them. Since in a parallelogram, opposite angles are equal. So \(\angle H=\angle L\))