Question

fall 2025 geometry b wwva
proving a quadrilateral is a parallelogram

in parallelogram lmno, what is the measure of angle n?

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. So, \((2x + 10)+(x + 20)=180\)

Step2: Solve the equation for \(x\)

$$
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$$

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

Substitute \(x = 50\) into \(\angle O=(x + 20)^{\circ}\), so \(\angle O=(50+20)^{\circ}=70^{\circ}\)

Step4: Use the property of opposite angles in a parallelogram

In a parallelogram, \(\angle N\) and \(\angle L\) are supplementary to \(\angle O\). Also, \(\angle N\) and \(\angle O\) are adjacent angles. Since \(\angle O = 70^{\circ}\), and adjacent angles in a parallelogram are supplementary (\(\angle N+\angle O=180^{\circ}\))

Answer:

\(110^{\circ}\)