In an equilateral triangle \( \triangle ABC \), the altitude from vertex \( A \) meets side \( BC \) at point \( D \). The measure of angle \( ADB \) is \( x \) degrees. If the measure of angle \( ACD \) is \( 60^\circ - x \) degrees, find the value of \( x \). Let's think step by step and output the final answer within \boxed{}.
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