Note the two triangles HLK and HFG.
Because triangles have 180 degrees, we can deduce that angle LHK is 75 degrees.
So the corner of H has an angle of 75 degrees for both triangles, HLK and HFG.
We also see that HF is double that of HL and HG is double that of HK.
That means we have two sides that are proportional to each other and their included angle is congruent. Thus, by the SAS similarity theorem, triangles HLK and HFG are similar.
If they are similar, then angle HLK is congruent to angle HFG.
Since angle HFG is 80 degrees, that makes angle HLK 80 degrees as well.