An isosceles triangle \( \triangle ABC \) has \( AB = AC \). The measure of \( \angle BAC \) is \( 40^\circ \). The triangle is extended by drawing a line from point \( A \) to point \( D \) such that \( \angle CAD \) is supplementary to \( \angle BAC \). What is the measure of \( \angle ABD \)? Let's think step by step and output the final answer within \boxed{}.
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