Question

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

Explanation:

Step1: Recall property of parallelogram

Adjacent angles of a parallelogram 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: $x = 50$.

Step3: Find the measure of $\angle N$

$\angle N=\angle L$ (opposite angles of a parallelogram are equal).
Substitute $x = 50$ into the expression for $\angle L$: $\angle L=2x + 10=2\times50+10=100 + 10=110^{\circ}$. So $\angle N = 110^{\circ}$.

Answer:

C. $110^{\circ}$