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

In the figure shown, triangle $C A E$ is similar to triangle $C B D$ . The measure of angle $C B D$ is $57 degree$ , and $upper A upper E equals 26 left parenthesis upper B upper D right parenthesis$ . What is the measure of angle $C A E$ ?

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Explanation

Choice C is correct. It's given that triangle $C A E$ is similar to triangle $C B D$ . Corresponding angles in similar triangles have equal measure. Angle $B C D$ and angle $A C E$ represent the same angle. It follows that angle $B C D$ and angle $A C E$ have equal measure and are corresponding angles. It's given in the figure that angle $B D C$ and angle $A E C$ are right angles and therefore have equal measure. It follows that angle $B D C$ and angle $A E C$ are corresponding angles. Therefore, angle $C B D$ and angle $C A E$ are corresponding angles and have equal measure. It's given that the measure of angle $C B D$ is $57 degree$ , so the measure of angle $C A E$ is $57 degree$ .

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.