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? Check all that apply.

3 = 6 = 98°
3 = 14 = 98°
4 = 8 = 82°
4 = 12 = 82°
5 = 8 = 82°

Answer 1

1, 3, 5 are the correct answers :)

Answer 2

Consider papallel lines c and d, lines b and a are transversals.

1. Angles 2 and 3 have equal measures, because they are vertical. Angles 3 and 6 are alternate interior angles, then ∠2=∠3=∠6=98°. Option 1 is correct.

2. ∠6=∠14, when a and b are parallel, but since a and b are not parallel, then ∠6≠∠14. Option 2 is incorrect.

3. Angles ∠4 and ∠8 are corresponding, then ∠4=∠8, because c and d are parallel. Angles ∠3 and ∠4 are complementary, then ∠4=180°-98°=82°. Then ∠4=∠8=82°. Option 3 is correct.

4. Angles ∠4 and ∠12 are corresponding, but they are not equal, because lines a and b are not parallel. Option 4 is incorrect.

5. Angles ∠5 and ∠8 are vertical, then they are equal. Angles ∠5 and ∠6 are complementary, then ∠5=180°-98°=82°. Then ∠5=∠8=82°. Option 5 is correct.

Answer: Options 1, 3, 5 are correct, options 2, 4 are incorrect.