Question

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

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, adjacent angles are supplementary, so $\angle L+\angle M = 180^{\circ}$. Here $\angle L=(25x)^{\circ}$ and $\angle N=(22x + 9)^{\circ}$, and $\angle L$ and $\angle N$ are adjacent angles. So $25x+22x + 9=180$.

Step2: Combine like - terms

Combine the $x$ terms: $(25x+22x)+9 = 180$, which simplifies to $47x+9 = 180$.

Step3: Solve for $x$

Subtract 9 from both sides: $47x=180 - 9=171$. Then $x=\frac{171}{47}$. But we assume there is a mistake and the angles $\angle L$ and $\angle N$ are opposite angles (opposite angles in a parallelogram are equal). So $25x=22x + 9$.

Step4: Solve the new equation for $x$

Subtract $22x$ from both sides: $25x-22x=22x + 9-22x$, which gives $3x=9$. Then $x = 3$.

Step5: Find measure of $\angle LMN$

If $x = 3$, and we assume we want to find an angle. If we consider the adjacent - angle relationship. Let's find $\angle LMN$. First, find $\angle L=(25x)^{\circ}$. Substitute $x = 3$, so $\angle L=75^{\circ}$. Since adjacent angles in a parallelogram are supplementary, $\angle LMN=180 - 75=105^{\circ}$.

Answer:

$105$