Question

M∠HGF=16x+4, m∠EGF=110 degrees, and m∠HGE=3x+11. Find x.

Answer 1

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.

Answer 2

I hope this helps you




16x+4=110+3x+11


13x=117


x=9