Difficult# Using Properties of Triangle Angles: Upping the Difficulty

GMAT-ETWBYN

In the diagram, triangle $JKI$ is an isosceles triangle with equal sides $JK$ and $IK$. Triangle $KIH$ is also isosceles, with equal sides $IK$ and $HK$.

Given that angle $J$ is $30$ degrees and angle $G$ is $40$ degrees,

what is the measure of angle $IKH$?