In the figure below, lines that appear to be parallel are parallel. Solve for a, b, and c.

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

yes

step-by-step explanation: