Given the figure, prove that ∠CAK > ∠G

Question

Note: Use Geometric Inequalities, Thank you

Answer 1

angle CAK = angle ACB + angle ABC

angle ABC = angle BOG + ang OGB where O is the intersection of HG and AB

angle CAK = angle ACB + angle BOG + angle OGB

therefore angle CAK > angle OGB

This may not be the proof you were looking for but it is correct.