Question

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

Explanation:

Step1: Recall parallelogram angle property

In a parallelogram, consecutive angles are supplementary (sum to \(180^\circ\)). So, \(\angle L + \angle O = 180^\circ\), which means \((x + 40) + 3x = 180\).

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 \(\angle O\)

\(\angle O = 3x\), substitute \(x = 35\): \(3 \times 35 = 105^\circ\).

Answer:

\(105^\circ\) (corresponding to the option "105°")