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

In the figure below, lines that appear to be parallel are parallel. Solve for a, b-example-1
User Khuram
by
3.9k points

1 Answer

5 votes

Answer:

a = 55

b = 13

c = 8

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

User Mike Holdsworth
by
4.3k points