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line AE and line DF are parallel. If m∠ABG = 11x and m∠HCF = 10x + 9, what is m∠ABG?

points B and C are on line GH between points G and H, line AE intersects with line GH at point B, line DF intersects with line GH at point C

102°
99°
81°
9°

Respuesta :

ken2004511

Answer:

81

Step-by-step explanation:

x=9

11x=99

11x+ABG=180⁰

ABG=81

akposevictor

Applying the alternate exterior angles theorem, m∠ABG = 99°

What is the Alternate Exterior Angles Theorem?

It states that alternate exterior angles, formed when a transversal cuts across two parallel lines, are congruent to each other. That is, they are of equal measure.

Since AE and DF are parallel, therefore:

m∠ABG = m∠HCF

  • Substitute

11x = 10x + 9

  • Subtract 10x from both sides

11x - 10x = 9

x = 9

Find m∠ABG = 11x

  • Plug in the value of x

m∠ABG = 11(9)

m∠ABG = 99°

Learn more about alternate exterior angles theorem on:

https://brainly.com/question/17883766

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