Question

Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°.

Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Where lines e and c intersect, the angles are: 1, 2, 4, 3. Where lines f and c intersect, the angles are 5, 6, 8, 7. Where lines e and d intersect, the angles are 9, 10, 12, 11. Where lines f and d intersect, the angles are 13, 14, 16, 15.
Which angle measures are correct? Select three options.

mAngle2 = 125°
mAngle3 = 55°
mAngle8= 55°
mAngle12 = 100°
mAngle14 = 100°

Answer 1

Correct: m∠2 = 125°, m∠8 = 55°, m∠14 = 100°.

Reasoning (brief):
- From m∠9 = 80° (at e∩d): vertical opposite ∠12 = 80°; adjacent ∠10 = 100°; corresponding at f∩d gives ∠13 = 80° and thus ∠14 = 100°.
- From m∠5 = 55° (at f∩c): vertical opposite ∠8 = 55°; corresponding at e∩c gives ∠1 = 55°, so ∠2 = 180° − 55° = 125° (and ∠3 = 125°).
- Therefore the true listed measures are ∠2 = 125°, ∠8 = 55°, ∠14 = 100°.