Question

in parallelogram lmno, what is the measure of angle n? (2x + 10)° (x + 20)° o 50° o 70° o 110° o 130°

Explanation:

Step1: Use property of parallelogram

In a parallelogram, adjacent angles are supplementary. So, $\angle L+\angle O = 180^{\circ}$.
$(2x + 10)+(x + 20)=180$.

Step2: Simplify the equation

Combine like - terms: $2x+x+10 + 20=180$, which gives $3x+30 = 180$.
Subtract 30 from both sides: $3x=180 - 30=150$.
Divide both sides by 3: $x=\frac{150}{3}=50$.

Step3: Find measure of $\angle N$

$\angle N$ and $\angle O$ are adjacent angles, so $\angle N=180^{\circ}-\angle O$.
Since $\angle O=x + 20$ and $x = 50$, then $\angle O=50+20 = 70^{\circ}$.
So, $\angle N=180 - 70=110^{\circ}$.

Answer:

$110^{\circ}$