Question

consider quadrilateral lmno.
if quadrilateral lmno is a parallelogram, what must the measure of
angle lmn be?
$m\angle lmn = \square$

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, consecutive angles are supplementary. So, \((25x)^{\circ}+(22x + 9)^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find \(\angle LMN\)

Since \(\angle LMN=\angle O\) (opposite angles of a parallelogram are equal), and \(\angle O=(25x)^{\circ}\). Substitute \(x = 3\) into \(\angle O\), we get \(\angle O=(25\times3)^{\circ}=75^{\circ}\).

Answer:

\(75\)