In trapezoid $ABCD$, $AD$ is parallel to $BC$, with the side lengths $AB = 6$, $BC = 7$, $CD = 8$, and $AD = 17$. If the sides $AB$ and $CD$ are extended to meet at point $E$, find the measure of the angle at $E$ (in degrees).

Let's think step by step and output the final answer within \boxed{}.
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