Question

figure lmno is a parallelogram. what is the value of x? 13 8 20 10

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, consecutive angles are supplementary. But here, we can also use the property that opposite angles are equal. Wait, no, for a parallelogram \(LMNO\), \(\angle M\) and \(\angle N\) are consecutive angles. So \(\angle M+\angle N = 180^{\circ}\) (since consecutive angles in a parallelogram are supplementary).
Given \(\angle M=(3x)^{\circ}\) and \(\angle N=(8x - 40)^{\circ}\), we have the equation \(3x+(8x - 40)=180\).

Step2: Simplify the equation

Combine like - terms: \(3x+8x-40 = 180\), which gives \(11x-40 = 180\).
Add \(40\) to both sides: \(11x-40 + 40=180 + 40\), so \(11x=220\).

Step3: Solve for \(x\)

Divide both sides by \(11\): \(x=\frac{220}{11}=8\).

Answer:

\(8\)