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

Right triangles $L M N$ and $P Q R$ are similar, where $L$ and $M$ correspond to $P$ and $Q$ , respectively. Angle $M$ has a measure of $53 degree$ . What is the measure of angle $Q$ ?

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Explanation

Choice B is correct. It’s given that triangle $L M N$ is similar to triangle $P Q R$ . Corresponding angles of similar triangles are congruent. Since angle $M$ and angle $Q$ correspond to each other, they must be congruent. Therefore, if the measure of angle $M$ is $53 degree$ , then the measure of angle $Q$ is also $53 degree$ .

Choice A is incorrect and may result from concluding that angle $M$ and angle $Q$ are complementary rather than congruent.

Choice C is incorrect and may result from concluding that angle $M$ and angle $Q$ are supplementary rather than congruent.

Choice D is incorrect and may result from conceptual or calculation errors.