Answer:
[tex]x=8[/tex]
[tex]\m\angle HFG= 80^\circ[/tex]
Step-by-step explanation:
Given that:
Point [tex]H[/tex] is interior of [tex]\angle EFG[/tex].
[tex]m\angle EFH = 75^\circ\\m\angle HFG = (10x)^\circ\\m\angle EFG = (20x-5)^\circ[/tex]
To find:
[tex]x = ?\\m\angle HFG = ?[/tex]
Solution:
First of all, let us represent the given values in the form of a diagram.
Kindly refer to the attached image for the given points and values of angles.
We can clearly see that:
[tex]m\angle EFG = m\angle EFH + m\angle HFG[/tex]
Putting all the values given in above equation, we get:
[tex](20x-5)^\circ = 75^\circ + 10x^\circ\\\Rightarrow 20x-10x=75+5\\\Rightarrow 10x =80\\\Rightarrow \bold{x =8}[/tex]
[tex]m\angle HFG =10x^\circ\\\Rightarrow m\angle HFG =10\times 8^\circ\\\Rightarrow m\angle HFG = \bold{80^\circ}[/tex]
