Question

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

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

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

Step2: Solve the equation for \(x\)

Combine like - terms: \(x+40 + 3x=180\), \(4x+40 = 180\). Subtract \(40\) from both sides: \(4x=180 - 40=140\). Divide by \(4\): \(x=\frac{140}{4}=35\).

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

Angle \(O=(3x)^{\circ}\). Substitute \(x = 35\) into \(3x\), so \(3x=3\times35 = 105\).

Answer:

\(105^{\circ}\)