Question

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

Explanation:

Step1: Check vertical angle of ∠5

∠5 and ∠3 are vertical angles, so \(m\angle3 = m\angle5 = 55^\circ\).

Step2: Check linear pair of ∠3

∠2 and ∠3 form a linear pair: \(m\angle2 = 180^\circ - 55^\circ = 125^\circ\).

Step3: Check vertical angle of ∠9

∠9 and ∠11 are vertical angles, so \(m\angle11 = 80^\circ\). ∠11 and ∠12 form a linear pair: \(m\angle12 = 180^\circ - 80^\circ = 100^\circ\).

Step4: Check corresponding angle of ∠5

∠5 and ∠13 are corresponding angles (parallel lines e,f; transversal c), so \(m\angle13 = 55^\circ\). ∠13 and ∠14 form a linear pair: \(m\angle14 = 180^\circ - 55^\circ = 125^\circ\) (not 100°). ∠5 and ∠7 form a linear pair: \(m\angle7 = 125^\circ\), so ∠8 (vertical to ∠7) is 125° (not 55°).

Answer:

m∠3 = 55°, m∠2 = 125°, m∠12 = 100°