Question

Show your work. Round to the nearest tenth if necessary. A. x=9 B. x=8.7 C. x=9.3

Answer 1

Given:

Line GH bisects angle FGI, that means angle FGH = angle HGI

To Find:

the value of x and angle FGI

Solution:

angle FGH = angle HGI

6x - 11 = 4x + 7

or, 6x - 4x = 7 + 11

or, 2x = 18

or, x = 18/2 = 9

angle FGI = angle FGH + angle HGI

or, angle FGI = 6x - 11 + 4x + 7

or, angle FGI = 10x - 4

By putting the value of x, we get

angle FGI = 10(9) - 4

or, angle FGI = 90 - 4 = 86°

Answer:

The value of x is 9.

Angle FGI = 86°