Answer/Step-by-step explanation:
1. If l is parallel to m, therefore:
58° and (5x - 2)° are Corresponding Angles.
Relationship: 58° = (5x - 2)°
Solve for x
58 = 5x - 2
Add 2 to both sides
58 + 2 = 5x - 2 + 2
60 = 5x
Divide both sides by 5
60/5 = 5x/5
12 = x
x = 12
2. If l is parallel to m, therefore:
134° and (16x + 22)° are Alternate Exterior Angles.
Relationship: 134° = (16x + 22)°
Solve for x
134° = 16x + 22°
Subtract 22 from both sides
134 - 22 = 16x + 22 - 22
112 = 16x
Divide both sides by 16
112/16 = 16x/16
7 = x
x = 7
3. (7x - 1)° and 125° are Alternate Interior Angles.
Relationship: (7x - 1)° = 125°
Solve for x
7x - 1 = 125
Add 1 to both side
7x = 125 + 1
7x = 126
Divide both sides by 7
x = 18
4. (9x + 2)° and 133° are Same Side Interior Angles.
Relationship: (9x + 2)° + 133° = 180° (supplementary)
Solve for x
9x + 2 + 133 = 180
9x + 135 = 180
9x = 180 - 135
9x = 45
x = 5
5. (8x - 77)° and (3x + 38)° are Alternate Exterior Angles
Relationship: (8x - 77)° = (3x + 38)°
Solve for x
8x - 77 = 3x + 38
8x - 3x = 77 + 38
5x = 115
x = 23
6. (11x - 47)° and (6x - 2)° are Corresponding Angles.
Relationship: (11x - 47)° = (6x - 2)°
Solve for x
11x - 47 = 6x - 2
11x - 6x = 47 - 2
5x = 45
x = 9
7. (13x - 21)° and (5x + 75)° are Alternate Interior Angles.
Relationship: (13x - 21)° = (5x + 75)°
Solve for x
13x - 21 = 5x + 75
13x - 5x = 21 + 75
8x = 96
Divide both sides by 8
8x/8 = 96/8
x = 12
8. (9x - 33)° and (5x + 3)° are Consecutive Exterior Angles
Relationship: (9x - 33)° + (5x + 3)° = 180°
Solve for x
9x - 33 + 5x + 3 = 180
14x - 30 = 180
14x = 180 + 30
14x = 210
x = 15
