Answer: The required value of x is 9.
Step-by-step explanation: We are given the following :
\(m\angle HGF=16x+4,~~~m\angle EGF=110^\circ~~~\textup{and}~~~m\angle HGE=3x+11.\)
We are to find the value of x.
From the figure, we note that
\(m\angle HGF=m\angle EGF+m\angle HGE\\\\\Rightarrow 16x+4=110+(3x+11)\\\\\Rightarrow 16x+4=3x+121\\\\\Rightarrow 16x-3x=121-4\\\\\Rightarrow 13x=117\\\\\Rightarrow x=\dfrac{117}{13}\\\\\Rightarrow x=9.\)
Thus, the required value of x is 9.
