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Geometry and Trigonometry Difficulty: Medium

The figure presents triangle A C E, where side A E is horizontal and vertex E is to the right of vertex A. Vertex C lies above side A E. Point B lies on side A C, point D lies on side C E, and line segment B D is drawn. A note states that the figure is not drawn to scale.

In the figure above, segments AE and BD are parallel. If angle BDC measures 58° and angle ACE measures 62°, what is the measure of angle CAE ?

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Explanation

Choice B is correct. It’s given that angle ACE measures $62 degrees$ . Since segments AE and BD are parallel, angles BDC and CEA are congruent. Therefore, angle CEA measures $58 degrees$ . The sum of the measures of angles ACE, CEA, and CAE is $180 degrees$ since the sum of the interior angles of triangle ACE is equal to $180 degrees$ . Let the measure of angle CAE be $x degrees$ . Therefore, $62 plus 58, plus x, equals 180$ , which simplifies to $x equals 60$ . Thus, the measure of angle CAE is $60 degrees$ .

Choice A is incorrect. This is the measure of angle AEC, not that of angle CAE. Choice C is incorrect. This is the measure of angle ACE, not that of CAE. Choice D is incorrect. This is the sum of the measures of angles ACE and CEA.