Question

2 solve for the following using the theorems/properties of a parallelogram. 12 cm 154° p o y l 16 cm po = cm ol = cm m∠y = m∠p =

Explanation:

Step1: Use the property of opposite sides of a parallelogram

In a parallelogram, opposite sides are equal. So, \(PO = YL\) and \(OL=PY\). Given \(YL = 16\mathrm{cm}\) and \(PY = 12\mathrm{cm}\).

• For \(PO\): \(PO=YL = 16\mathrm{cm}\)
• For \(OL\): \(OL = PY=12\mathrm{cm}\)

Step2: Use the property of consecutive angles of a parallelogram

In a parallelogram, consecutive angles are supplementary (\(\angle O+\angle L = 180^{\circ}\), \(\angle Y+\angle L=180^{\circ}\), \(\angle P+\angle O = 180^{\circ}\)). Given \(\angle L=154^{\circ}\)

• For \(m\angle Y\): Since \(\angle Y+\angle L = 180^{\circ}\), then \(m\angle Y=180^{\circ}- 154^{\circ}=26^{\circ}\)
• For \(m\angle P\): Since \(\angle P+\angle O=180^{\circ}\), and \(\angle O=\angle L = 154^{\circ}\) (opposite angles of a parallelogram are equal), then \(m\angle P=180^{\circ}-154^{\circ} = 26^{\circ}\)

Answer:

\(PO = 16\mathrm{cm}\)
\(OL = 12\mathrm{cm}\)
\(m\angle Y=26^{\circ}\)
\(m\angle P = 154^{\circ}\)