Question

myra took a picture of the sky one afternoon when two jet airplanes appeared to draw a pair of parallel lines with their vapor trails. the vapor trails from two other jets flying from another direction crossed over the parallel trails. she printed her picture and labeled the angles and lines. assume lines c and d are parallel and ∠2 measures 98°. which statements are true? select three options. □m∠3 = m∠8 = 98° □m∠3 = m∠14 = 98° □m∠4 = m∠8 = 82° □m∠4 = m∠12 = 82° □m∠5 = m∠8 = 82°

Explanation:

Step1: Use vertical angles property

Since \(\angle2\) and \(\angle3\) are vertical angles, \(m\angle3 = m\angle2=98^{\circ}\). Also, \(\angle3\) and \(\angle14\) are alternate - interior angles (because lines \(c\) and \(d\) are parallel and the transversal cuts them). By the alternate - interior angles theorem, \(m\angle3=m\angle14 = 98^{\circ}\).

Step2: Use linear - pair and corresponding angles properties

Since \(\angle2\) and \(\angle4\) form a linear pair (\(\angle2+\angle4 = 180^{\circ}\)), \(m\angle4=180 - 98=82^{\circ}\). \(\angle4\) and \(\angle8\) are corresponding angles (because lines \(c\) and \(d\) are parallel and the transversal cuts them). By the corresponding angles theorem, \(m\angle4=m\angle8 = 82^{\circ}\). \(\angle4\) and \(\angle12\) are not related by any of the parallel - line angle theorems (they are not corresponding, alternate - interior, or alternate - exterior angles). \(\angle5\) and \(\angle8\) are not equal. \(\angle5\) and \(\angle7\) are vertical angles, and \(\angle7\) and \(\angle8\) form a linear pair (\(m\angle7 + m\angle8=180^{\circ}\)).

Answer:

\(m\angle3 = m\angle14 = 98^{\circ}\), \(m\angle4 = m\angle8 = 82^{\circ}\), \(m\angle3 = m\angle8 = 98^{\circ}\)