Question

what is the measure of angle o in parallelogram lmno? (x + 40)° (3x)° o 35° o 75° o 105° o 155

Explanation:

Step1: Recall property of parallelogram

Adjacent angles in a parallelogram are supplementary, so $(x + 40)+3x=180$.

Step2: Combine like - terms

$x+3x + 40=180$, which simplifies to $4x+40 = 180$.

Step3: Solve for $x$

Subtract 40 from both sides: $4x=180 - 40=140$. Then divide both sides by 4, so $x=\frac{140}{4}=35$.

Step4: Find measure of angle O

Angle O is $3x$. Substitute $x = 35$ into $3x$, we get $3\times35 = 105$.

Answer:

$105^{\circ}$