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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Easy

The figure presents triangle B A, C, such that side B C is horizontal and vertex A, is above side B C. Angle A, is labeled x degrees.

In the given triangle, $the length of side A, B equals the length of side A, C$ and $angle A, B C$ has a measure of $67 degrees$ . What is the value of x ?

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Explanation

Choice B is correct. Since $the length of A, B equals the length of A, C$ , the measures of their corresponding angles, $angle A, B C$ and $angle A, C B$ , are equal. Since $angle A, B C$ has a measure of $67 degrees$ , the measure of $angle A, C B$ is also $67 degrees$ . Since the sum of the measures of the interior angles in a triangle is $180 degrees$ , it follows that $67 plus 67, plus x, equals 180$ , or $134 plus x, equals 180$ . Subtracting by 134 on both sides of this equation yields $x equals 46$ .

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