SOLUTION: Hello there my question is Ray GJ bisects < FGH, m < FGJ = (7x - 9)°, and m < HGJ = (2x + 36)°. What is m < FGH?

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Question 1196606: Hello there my question is
Ray GJ bisects < FGH, m < FGJ = (7x - 9)°, and m < HGJ = (2x + 36)°. What is m < FGH?
Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
.

Since angle FGH is bisected by the ray GJ, its halves, angles FGJ and HGJ are congruent 
and, therefore, have equal angular measures.  THEREFORE, we can write this equation

      7x - 9 = 2x + 36.


From this equation

    7x - 2x = 36 + 9

       5x   =   45

        x   =   45/5 = 9 degrees.


From it, we deduce  m < FGJ = 7x-9 = 7*9-9 = 63-9 = 54 degrees.


Angle's FGH angular measure is twice of it, i.e. 54*2= 108 degrees.    ANSWER

Solved, with full explanations.



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