Question

line AE and line DF are parallel. If m∠ABG = 12x and m∠HCF = 11x + 9, what is m∠HCF?

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

15°
72°
108°
112°

Answer 1

Answer:

Answer is 108

Answer 2

This question is incomplete without figure; find the figure in the attachment.

  Option (3) will be the correct option.    

    Given in the question,

• m∠ABG = 12x
• m∠HCF = 11x + 9
• AE║DF and a line GH intersects the these parallel lines at B and C respectively.

Since, AE║DF and a line GH intersects the these parallel lines at B and C,

∠ABG ≅ ∠HCF  [Alternate exterior angles]

12x = 11x + 9

12x - 11x = 9

x = 9

By substituting the value of 'x' in the measure of the angle,

m∠HCF = 11x + 9

             = 11(9) + 9

             = 108°

     Therefore, Option (3) will be the correct option.

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