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

Quadrilateral $P^{'} Q^{'} R^{'} S^{'}$ is similar to quadrilateral $P Q R S$ , where $P$ , $Q$ , $R$ , and $S$ correspond to $P^{'}$ , $Q^{'}$ , $R^{'}$ , and $S^{'}$ , respectively. The measure of angle $P$ is $30 degree$ , the measure of angle $Q$ is $50 degree$ , and the measure of angle $R$ is $70 degree$ . The length of each side of $P^{'} Q^{'} R^{'} S^{'}$ is $3$ times the length of each corresponding side of $P Q R S$ . What is the measure of angle $P^{'}$ ?

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Explanation

Choice B is correct. It's given that quadrilateral $P^{'} Q^{'} R^{'} S^{'}$ is similar to quadrilateral $P Q R S$ , where $P$ , $Q$ , $R$ , and $S$ correspond to $P^{'}$ , $Q^{'}$ , $R^{'}$ , and $S^{'}$ , respectively. Since corresponding angles of similar quadrilaterals are congruent, it follows that the measure of angle $P$ is equal to the measure of angle $P^{'}$ . It's given that the measure of angle $P$ is $30 degree$ . Therefore, the measure of angle $P^{'}$ is $30 degree$ .

Choice A is incorrect. This is $\frac{1}{3}$ the measure of angle $P^{'}$ .

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

Choice D is incorrect. This is $3$ times the measure of angle $P^{'}$ .