Answer:
[tex] m\angle EFG = 52\degree[/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex] m\angle EFG =\frac{1}{2} m\angle EDG[/tex]
[tex] (x+51)\degree =\frac{1}{2}(10x +94)\degree [/tex]
[tex] (x+51)\degree =\frac{1}{2}\times 2(5x +47)\degree [/tex]
[tex] (x+51)\degree =(5x +47)\degree [/tex]
[tex] x+51 =5x +47 [/tex]
[tex] x+51 - 47=5x - x[/tex]
[tex] 4=4x[/tex]
[tex] x=\frac{4}{4}[/tex]
[tex] x=1[/tex]
[tex] \because m\angle EFG = (x+51)\degree[/tex]
[tex]\therefore m\angle EFG = (1+51)\degree[/tex]
(plug x = 1)
[tex] \therefore m\angle EFG = 52\degree[/tex]
