Answer:
a = 55
b = 13
c = 8
Step-by-step explanation:
2a - 5 = 105° (alternate exterior angles are congruent)
Add 5 to both sides
2a - 5 + 5 = 105 + 5
2a = 110
Divide both sides by 2
2a/2 = 110/2
a = 55
(2a - 5) + (5b + 10) = 180° (consecutive interior angles/same side interior are supplementary)
Plug in the value of a
2(55) - 5 + 5b + 10 = 180
110 - 5 + 5b + 10 = 180
Add like terms
115 + 5b = 180
Subtract 115 from each side
115 + 5b - 115 = 180 - 115
5b = 65
Divide both sides by
5b/5 = 65/5
b = 13
10c - 5 = 5b + 10 (corresponding angles are congruent)
Plug in the value of b
10c - 5 = 5(13) + 10
10c - 5 = 65 + 10
10c - 5 = 75
Add 5 to both sides
10c - 5 + 5 = 75 + 5
10c = 80
Divide both sides by 10
10c/10 = 80/10
c = 8
