Question

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

Explanation:

Step1: Use property of parallelogram

In a parallelogram, consecutive angles are supplementary. So, \((x + 40)+3x=180\).

Step2: Solve for \(x\)

Combine like terms: \(4x+40 = 180\).
Subtract \(40\) from both sides: \(4x=180 - 40=140\).
Divide by \(4\): \(x=\frac{140}{4}=35\).

Step3: Find measure of \(\angle O\)

Since \(\angle O = 3x\), substitute \(x = 35\). So, \(\angle O=3\times35 = 105^{\circ}\).

Answer:

\(105^{\circ}\) (corresponding to the third option in the given multiple - choice list)