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PLEASE SOLVE!! I just need to know each of the variables value in the image. Your help is immensely appreciated. (10c + d)° (5b - 5c)°\(2d + 6e)° (a + 2b)° (4f + 4e)° (a + 30)°

PLEASE SOLVE!! I just need to know each of the variables value in the image. Your-example-1
User Felene
by
7.5k points

1 Answer

4 votes

Answer:

a = 30

b = 15

c = 3

d = 30

e = 10

f = 20

Explanation:

According to the Alternate Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the alternate sides of the transversal are congruent. Therefore:

(a + 30)° = 60°

a + 30 = 60

a = 30

According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent. Therefore:

(a + 30)° = (a + 2b)°

a + 30 = a + 2b

30 = 2b

b = 15

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent. Therefore:

(a + 2b)° = (5b - 5c)°

(30 + 2(15))° = (5(15) - 5c)°

60° = (75 - 5c)°

60 = 75 - 5c

5c = 75 - 60

5c = 15

c = 3

According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent. Therefore:

(a + 2b)° = (10c + d)°

(30 + 2(15))° = (10(3) + d)°

60° = (30 + d)°

60 = 30 + d

d = 30

Angles on a straight line sum to 180°. Therefore:

(a + 2b)° + (2d + 6e)° = 180°

(30 + 2(15))° + (2(30) + 6e)° = 180°

60° + (60 + 6e)° = 180°

60 + 60 + 6e = 180

120 + 6e = 180

6e = 60

e = 10

According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°). Therefore:

(a + 2b)° + (4f + 4e)° = 180°

(30 + 2(15))° + (4f + 4(10))° = 180°

60° + (4f + 40)° = 180°

60 + 4f + 40 = 180

100 + 4f = 180

4f = 80

f = 20

User Andrew Allen
by
7.6k points

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