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Lines b and c are parallel.

Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: (13 x + 9) degrees, 2, 4, 3. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, (5 x + 9) degrees, 8.
What is the measure of Angle6?

mAngle6 = 45°
mAngle6 = 54°
mAngle6 = 117°
mAngle6 = 126°

Respuesta :

calculista

Answer:

[tex]m\angle 6=54^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the value of x

we know that

[tex](13x+9)^o+(5x+9)^o=180^o[/tex] ----> by consecutive exterior angles (supplementary angles)

solve for x

[tex](18x+18)^o=180^o\\18x=162\\x=9[/tex]

step 2

Find the measure of angle 6

we know that

[tex]m\angle 6=(5x+9)^o[/tex] ----> by vertical angles

substitute the value of x

[tex]m\angle 6=(5(9)+9)=54^o[/tex]

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abidemiokin

Option B is correct. The measure of angle 6 is  54 degrees

First, we must know that the sum of exterior angles are supplementary. Hence;

  • 5x+9 + 13x+9 = 180

Get the value of x;

5x + 13x + 9 + 9 = 180

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 162/18

x = 9

Get the measure of angle 6;

m<6 = 5x + 9 (vertical angles)

m<6 = 5(9) + 9

m<6 = 45 + 9

m<6 = 54 degrees

Hence the measure of angle 6 is  54 degrees

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