What is the measure of Angel G?

[Cheychey23]

I have been stuck on this question for a while , um i think you take half of angle L which would be Angle F and a triangle needs to be 180* so im stuck !

 

[blamocur]

What do you know about angles in similar triangles?

 

[pka]

I have been stuck on this question for a while , um i think you take half of angle L which would be Angle F and a triangle needs to be 180* so im stuck !

This may be disputed but it is what modem axiomatic geometry textbooks teach.
In order for [imath]\Delta ABC\sim \Delta XYZ[/imath] it must be the case that angles [imath]\angle A\cong\angle X~\&~\angle B\cong\angle Y [/imath]
Thus in your problem it must be the case that [imath]\angle H\cong\angle N~\&~\angle F\cong\angle L [/imath].
Because the sum of the angular measures is [imath]180^o [/imath], what is [imath]m(\angle G)=~? [/imath]