Question

lmno is a parallelogram, with ∠m=(11x)° and ∠n=(6x - 7)°. which statements are true about parallelogram lmno? choose three correct answers.
□ m∠l = 22°
□ m∠m = 111°
□ m∠n = 59°
□ x = 11
□ m∠o = 121°

Explanation:

Step1: Use adjacent - angles property

In a parallelogram, adjacent angles are supplementary, so $\angle M+\angle N = 180^{\circ}$. Substitute the given angle measures: $(11x)+(6x - 7)=180$.

Step2: Solve the equation for $x$

Combine like - terms: $11x+6x-7 = 180$, which simplifies to $17x-7 = 180$. Add 7 to both sides: $17x=180 + 7=187$. Then divide both sides by 17: $x=\frac{187}{17}=11$.

Step3: Find the measure of $\angle M$

Substitute $x = 11$ into the measure of $\angle M$: $m\angle M=11x=11\times11 = 121^{\circ}$.

Step4: Find the measure of $\angle N$

Substitute $x = 11$ into the measure of $\angle N$: $m\angle N=6x - 7=6\times11-7=66 - 7 = 59^{\circ}$.

Step5: Use opposite - angles property

In a parallelogram, opposite angles are equal. So $m\angle M=m\angle O = 121^{\circ}$ and $m\angle N=m\angle L = 59^{\circ}$.

Answer:

$x = 11$, $m\angle N = 59^{\circ}$, $m\angle O = 121^{\circ}$