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Geometry and Trigonometry Difficulty: Hard

Triangle $X Y Z$ is similar to triangle $R S T$ such that $X$ , $Y$ , and $Z$ correspond to $R$ , $S$ , and $T$ , respectively. The measure of $∠ Z$ is $20 degree$ and $2 upper X upper Y equals upper R upper S$ . What is the measure of $∠ T$ ?

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Explanation

Choice C is correct. It’s given that triangle $X Y Z$ is similar to triangle $R S T$ , such that $X$ , $Y$ , and $Z$ correspond to $R$ , $S$ , and $T$ , respectively. Since corresponding angles of similar triangles are congruent, it follows that the measure of $∠ Z$ is congruent to the measure of $∠ T$ . It’s given that the measure of $∠ Z$ is $20 degree$ . Therefore, the measure of $∠ T$ is $20 degree$ .

Choice A is incorrect and may result from a conceptual error.

Choice B is incorrect. This is half the measure of $∠ Z$ .

Choice D is incorrect. This is twice the measure of $∠ Z$ .