what is the measure of angle o in parallelogram lmno? 35° 75° 105° 155

Explanation:

Step1: Use property of parallelogram

In a parallelogram, adjacent - angles are supplementary. So, $\angle L+\angle O = 180^{\circ}$. Given $\angle L=(x + 40)^{\circ}$ and $\angle O=(3x)^{\circ}$, we have the equation $(x + 40)+3x=180$.

Step2: Solve the equation for x

Combine like - terms: $x+3x+40 = 180$, which simplifies to $4x+40 = 180$. Subtract 40 from both sides: $4x=180 - 40=140$. Then divide both sides by 4: $x=\frac{140}{4}=35$.

Step3: Find the measure of angle O

Substitute $x = 35$ into the expression for $\angle O$. $\angle O=(3x)^{\circ}$, so $\angle O=3\times35^{\circ}=105^{\circ}$.

Answer:

$105^{\circ}$