Question

consider quadrilateral lmno. if quadrilateral lmno is a parallelogram, what must the measure of angle lmn be? ( mangle 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: \(25x+22x+9 = 180\), 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 \(\angle LMN=22x + 9\), substitute \(x = 3\) into the expression.
\(\angle LMN=22\times3+9=66 + 9=75\).

Answer:

\(75\)