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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 $IKH$?

A

$120$ degrees

B

$20$ degrees

C

$40$ degrees

D

$30$ degrees

E

Not enough information is given.

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