Question

Horizontal and parallel lines e and f are cut by transversals c and d. All angles are described clockwise, from uppercase left. The intersection of lines d and c form angles: 1, 2, 4, 3. The intersection of lines f and c form angles 5, 6, 8, 7. The intersection of lines e and d form angles 9, 10, 12, 11. The intersection of lines f and d form angles 13, 14, 16, 15.
In the diagram, m∠3 = 120° and m∠12 = 80°. Which angle measures are correct? Check all that apply.

m∠1 = 60°
m∠13 = 80°
m∠6 = 80°
m∠5 = 60°
m∠10 = 120°
m∠ 14 = 100°

Answer 1

Answers that are correct: m∠1 = 60°, m∠13 = 80°, m∠14 = 100°.

Work:
- At the intersection of c and d (angles 1,2,4,3) m∠3 = 120° so its vertical angle m∠2 = 120° and the adjacent angles m∠1 and m∠4 = 60°. Hence m∠1 = 60° (true).
- At the intersection of e and d (angles 9,10,12,11) m∠12 = 80° so its vertical m∠9 = 80° and the adjacent m∠10 and m∠11 = 100°.
- e and f are parallel, so corresponding angles at f and d equal those at e and d: m∠13 corresponds to m∠9, so m∠13 = 80° (true); m∠14 corresponds to m∠10, so m∠14 = 100° (true).
- The remaining choices (m∠6 = 80°, m∠5 = 60°, m∠10 = 120°) are not consistent with the above results.