Answer:
x = 5
[tex] m\angle DEF = 90\degree [/tex]
Step-by-step explanation:
GE is the angle bisector of quadrilateral DEFG,
Thus, by angle bisector property:
9x°= (5x + 20)°
9x = 5x + 20
9x - 5x = 20
4x = 20
x = 20/4
x = 5
[tex] m\angle DEF = 9x\degree + (5x+20)\degree [/tex]
[tex] m\angle DEF = (14x+20)\degree [/tex]
[tex] m\angle DEF = (14\times 5+20)\degree [/tex]
[tex] m\angle DEF = (70+20)\degree [/tex]
[tex] m\angle DEF = 90\degree [/tex]
