Answer:
[tex]m\angle DHG=72 \°[/tex].
Step-by-step explanation:
Given [tex]m\angle DHG=6(x-2) \°\\m\angle EHF=(3x+30) \°[/tex]
When two lines intersect each other then the angles formed by intersecting is called opposite angle also known as vertical angle as they share the same corner and they are congruent means they are equal.
Here line segment DF and EG intersect each other at point H.
Therefore ∠DHG and ∠EHF are opposite angles whose measure is equal.`
So, [tex]m\angle DHG=m\angle EHF\\6(x-2)=3x+30\\6x-12=3x+30\\6x-3x=30+12\\3x=42\\x=14[/tex]
Now, [tex]m\angle DHG=6(x-2) \°[/tex]
Substituting the value of x we will get the measure of ∠DHG.
[tex]m\angle DHG=6(x-2) \° = 6(14-2) \° = (6\times12) \°=72 \°[/tex]
Thus the measure of ∠DHG is 72°.
