In the given figure of quadrilateral FGHI,
Line FH and IG are the diagonals that bisect the angles :
FH divide the angles GHI and IFG
IG divide the angles FGH and FIH
Since, FH divide the angle IFG such that , Angle IFG = Angle IFJ + Angle JFG
where, Angle IFJ = AngleJFG
Substitute the value :
5x - 1 = 2x + 11
Simplify the equation for x :
5x - 2x = 11 + 1
3x = 12
x = 12/3
x = 4
Substiute the value of x = 4 in the the angle JFG
as JFG = 2x + 11
Angle JFG = 2(4) + 11
Angle JFG = 8 + 11
Angle JFG = 19
Angle FJG = 90 degree,
In the triangle, FJG,
The sum of all angles in the triangle is equal 180 degree
Angle FJG + Angle JFG + Angle FGJ = 180
90 + 19 + Angle FGJ = 180
109 + Angle FGJ = 180
Angle FGJ = 180 - 109
Angle FGJ = 71 degree
Answer : m