Question

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

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

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

Step2: Solve the equation for \(x\)

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

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

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

Answer:

\(105^{\circ}\) (corresponds to the third option \(105^{\circ}\))