Refer to the image below.
QUESTION A
The 123° angle and < 1 are corresponding angles.
Therefore, < 1 = 123°.
< 1 and < 2 are vertical angles.
Therefore, < 2 = 123°.
QUESTION B
The 71° angle and < 1 are consecutive interior angles.
Therefore, < 1 + 71° = 180°.
Subtract 71 from 180 to find that < 1 = 109°.
The 71° angle and < 2 are supplementary.
Therefore, < 2 + 71° = 180°.
Subtract 71 from 180...< 2 = 109°.
(You could also find < 2 by the fact that it and < 1 are alternate interior angles.)
QUESTION C
m < 1 = 53°
By vertical, alternate interior, and alternate exterior:
m < 3, 5, 7, 9, 11, 13, and 15 = 53°
By supplementary or consecutive interior angles:
180 - 53 = 127
m < 2, 4, 6, 8, 10, 12, 14, and 16 = 127°
QUESTION D
Keep in mind there's not really a specific order for doing these. It's just applying the rules to find angles one by one.
< 1 = 39°
1 and 3 are vertical. < 3 = 39°.
1 and 2 are supplementary. 180 - 39 = < 2 = 141°.
2 and 4 are vertical. < 4 = 141°.
2 and 5 are consecutive interior. 180 - 141 = < 5 = 39°.
5 and 7 are vertical. < 7 = 39°.
5 and 6 are complementary. 90 - 39 = < 6 = 51°.
6 and 8 are vertical. < 8 = 51°.
9 is vertical to a right angle. < 9 = 90°.
8 and 10 are alternate interior. < 10 = 51°.
10 and 13 are vertical. < 13 = 51°.
13 and 11 are complementary. 180 - 51 = < 11 = 141°.
11 and 12 are vertical. < 12 = 141°.