Question

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

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. So, \(25x+(22x + 9)=180\)

Step2: Solve the equation for \(x\)

Combine like - terms: \(25x+22x+9 = 180\), \(47x+9=180\)
Subtract 9 from both sides: \(47x=180 - 9\), \(47x=171\)
Divide both sides by 47: \(x = 3\)

Step3: Find the measure of \(\angle LMN\)

Since \(\angle LMN\) and \(\angle O\) are adjacent angles (\(\angle O=(25x)^{\circ}\)), and we know \(x = 3\)
\(\angle LMN=180-(25x)^{\circ}\)
Substitute \(x = 3\) into the formula: \(\angle LMN=180 - 25\times3\)
\(\angle LMN=180-75\)

Answer:

\(105\)