If triangle $$ACD$$ is equilateral and triangle $$ACB$$ is right as shown above, what is the value of $$x^\circ$$?

Correct.
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Given that $$AC = AD = CD$$, triangle $$ACD$$ is an equilateral triangle with all three angles equal to $$\frac{180^\circ}{3} = 60^\circ$$. So
>$$x^\circ = 180^\circ - \angle ACB - \angle DAC = 180^\circ - 90^\circ - 60^\circ = 30^\circ$$.

Incorrect.
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You might have gotten this answer if you found $$\angle CDB$$ instead of $$\angle CBD$$.

Incorrect.
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Carefully check your calculations.

Incorrect.
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This is the measures of the angles in triangle $$ACD$$, not the value of $$x$$.

Incorrect.
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Carefully check your work.

30°

45°

60°

90°

120°