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In the given triangle, $AB=AC$ and $\\angle ABC$ has a measure of $67^{\\circ}$. What is the value of $x$?

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In the given triangle, $AB=AC$ and $\\angle ABC$ has a measure of $67^{\\circ}$. What is the value of $x$?

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Choice B is correct. Since $AB=AC$, the measures of their corresponding angles, $ \\angle ABC$ and $ \\angle ACB$, are equal. Since $ \\angle ABC$ has a measure of $67^{\\circ}$, the measure of $ \\angle ACB$ is also $67^{\\circ}$. Since the sum of the measures of the interior angles in a triangle is $180^{\\circ}$, it follows that $67+67+x=180$, or $134+x=180$. Subtracting by $134$ on both sides of this equation yields $x=46$.

Choices A, C, and D are incorrect and may result from calculation errors.

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In the given triangle, $AB=AC$ and $\\angle ABC$ has a measure of $67^{\\circ}$. What is the value of $x$?

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In the given triangle, $AB=AC$ and $\angle ABC$ has a measure of $67^{\circ}$. What is the value of $x$?