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Lines, angles, and triangles SAT question
Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.
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 ?
ExplanationShow
Choice B is correct. It’s given that angle ACE measures 
. Since segments AE and BD are parallel, angles BDC and CEA are congruent. Therefore, angle CEA measures 
. The sum of the measures of angles ACE, CEA, and CAE is 
since the sum of the interior angles of triangle ACE is equal to . Let the measure of angle CAE be 
. Therefore, 
, which simplifies to 
. Thus, the measure of angle CAE is 
.
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.
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