MediumMath· Geometry and Trigonometry· Lines, angles, and triangles· MCQ
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 ?
A
58°
B
60°
C
62°
D
120°
Correct answer: B
Explanation
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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id cb_question_bank:b954d190-3e95-4dc3-99ff-0ad88a319ecc · question 6dd463ca · IBN 029403-DC
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