Question

lines e and f are parallel. the m∠9 = 80° and m∠5 = 55°. which angle measures are correct? select three options. m∠2 = 125° m∠3 = 55° m∠8 = 55° m∠12 = 100° m∠14 = 100°

Explanation:

Step1: Use corresponding - angle property

Since lines \(e\) and \(f\) are parallel, \(\angle3\) and \(\angle5\) are corresponding angles. So \(m\angle3=m\angle5 = 55^{\circ}\).

Step2: Use vertical - angle property

\(\angle5\) and \(\angle8\) are vertical angles. Vertical angles are equal, so \(m\angle8=m\angle5 = 55^{\circ}\).

Step3: Use linear - pair and corresponding - angle properties

\(\angle9\) and \(\angle12\) are corresponding angles. So \(m\angle12=m\angle9 = 80^{\circ}\). \(\angle9\) and \(\angle10\) form a linear - pair (\(m\angle9 + m\angle10=180^{\circ}\)), \(m\angle10 = 100^{\circ}\), and \(\angle10\) and \(\angle14\) are corresponding angles, so \(m\angle14=m\angle10 = 100^{\circ}\). Also, \(\angle2\) and \(\angle5\) are same - side interior angles. \(m\angle2 + m\angle5=180^{\circ}\), \(m\angle2=125^{\circ}\).

Answer:

A. \(m\angle2 = 125^{\circ}\)
B. \(m\angle3 = 55^{\circ}\)
C. \(m\angle8 = 55^{\circ}\)