we know that
Vertical angles are a pair of opposite and congruent angles formed by intersecting lines
so
Step 1
Find the value of x
[tex][6(x-2)]\°=(3x+30)\°[/tex] ------> by vertical angles
[tex]6x-12=3x+30\\6x-3x=30+12\\3x=42\\x=14\°[/tex]
Step 2
Find the value of m∠DHG
m∠DHG=[tex][6(x-2)]\°[/tex]
substitute the value of x
m∠DHG=[tex][6*(14-2)]\°[/tex]
m∠DHG=[tex][6*(12)]\°[/tex]
m∠DHG=[tex]72\°[/tex]
therefore
the answer is
m∠DHG=[tex]72\°[/tex]
