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

For the triangles shown, triangle $A B C$ is dilated by a scale factor of $3$ to obtain triangle $X Y Z$ , where $d equals 16$ . What is the measure, in degrees, of angle $X$ ?

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Explanation

Choice C is correct. It's given that triangle $X Y Z$ is obtained by a dilation of triangle $A B C$ . It follows that triangle $A B C$ is similar to triangle $X Y Z$ , where $A$ corresponds to $X$ . Since corresponding angles in similar triangles have the same measure and the measure of angle $A$ is $60$ degrees, it follows that the measure of angle $X$ is also $60$ degrees.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.