Answer:
[tex] w = 7 [/tex]
Step-by-step explanation:
Given:
m<FGK = (7w + 3)°
m<FGH = 104°
angle bisector of <FGH = GK
Required:
Value of w
SOLUTION:
Since GK bisects angle FGH, it divides the angle into two equal parts. Therefore, the following equation can be generated to find the value of w:
m<FGH = 2*m<FGK
[tex] 104 = 2*(7w + 3) [/tex] (substitution)
Divide both sides by 2
[tex] \frac{104}{2} = \frac{2*(7w + 3)}{2} [/tex]
[tex] 52 = 7w + 3 [/tex]
Subtract 3 from each side
[tex] 52 - 3 = 7w + 3 - 3 [/tex]
[tex] 49 = 7w [/tex]
Divide both sides by 7
[tex] \frac{49}{7} = \frac{7w}{7} [/tex]
[tex] 7 = w [/tex]
[tex] w = 7 [/tex]
