Question

lines e and f are parallel. the m∠9 = 80° and m∠3 = 55°. which angle measures are correct? choose three correct answers. m∠2 = 125° m∠12 = 100° m∠8 = 55° m∠3 = 55° m∠14 = 100°

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle3 = 55^{\circ}\) and \(\angle2+\angle3 = 180^{\circ}\) (linear - pair), then \(m\angle2=180 - 55=125^{\circ}\).

Step2: Find \(m\angle12\)

Since \(m\angle9 = 80^{\circ}\) and \(\angle9+\angle10 = 180^{\circ}\) (linear - pair), \(m\angle10 = 100^{\circ}\). Also, \(\angle10\) and \(\angle12\) are vertical angles. So \(m\angle12=m\angle10 = 100^{\circ}\).

Step3: Find \(m\angle8\)

\(\angle3\) and \(\angle8\) are alternate - exterior angles. Since lines \(e\) and \(f\) are parallel, \(m\angle8=m\angle3 = 55^{\circ}\).

Step4: Check \(m\angle3\)

Given \(m\angle3 = 55^{\circ}\).

Step5: Find \(m\angle14\)

\(\angle10\) and \(\angle14\) are corresponding angles. Since lines \(e\) and \(f\) are parallel, \(m\angle14=m\angle10 = 100^{\circ}\).

Answer:

\(m\angle2 = 125^{\circ}\), \(m\angle12 = 100^{\circ}\), \(m\angle8 = 55^{\circ}\), \(m\angle3 = 55^{\circ}\), \(m\angle14 = 100^{\circ}\) are all correct. But if we choose three: \(m\angle2 = 125^{\circ}\), \(m\angle8 = 55^{\circ}\), \(m\angle14 = 100^{\circ}\)