Question

consider quadrilateral lmno. if quadrilateral lmno is a parallelogram, what must the measure of angle lmn be? ( mangle lmn=)

Explanation:

Step1: Use the property of parallelogram adjacent angles

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

Step2: Solve the equation for \(x\)

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

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

Since \(\angle L\) and \(\angle LMN\) are adjacent angles in a parallelogram (\(\angle L = 25x\) and \(x = 3\)), \(\angle L=25\times3 = 75^{\circ}\).
Using the supplementary property (\(\angle L+\angle LMN=180^{\circ}\)), then \(\angle LMN=180 - 75=105^{\circ}\).

Answer:

\(105\)