Question

in parallelogram lmno, what is the measure of angle n? 50° 70° 110° 130°

Explanation:

Step1: Use property of parallelogram

Adjacent angles of a parallelogram are supplementary. So, \((2x + 10)+(x + 20)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+x+10 + 20=180\), which gives \(3x+30 = 180\).

Step3: Solve for \(x\)

Subtract 30 from both sides: \(3x=180 - 30=150\). Then divide both sides by 3, so \(x = 50\).

Step4: Find the measure of angle \(N\)

Angle \(N\) and angle \(O\) are adjacent. Angle \(O=x + 20\). Substitute \(x = 50\) into the expression for angle \(O\), we get angle \(O=50+20 = 70^{\circ}\). Since angle \(N\) and angle \(O\) are supplementary, angle \(N=180 - 70=110^{\circ}\).

Answer:

C. \(110^{\circ}\)