Modded SAT Question Bank
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Test
Math
Domain
Geometry and Trigonometry
Skill
Lines, angles, and triangles
Difficulty
Medium
ID: 6dd463ca
Modded SAT Question Bank by Abdullah Mallik
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 ?

  1. 58°

  2. 60°

  3. 62°

  4. 120°

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Correct Answer: B
Rationale

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.

Question Difficulty: Medium
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