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Lines, angles, and triangles SAT question

Math · Geometry and Trigonometry · Easy · Answer it here, explanation included.

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 ?

ExplanationShow

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.

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