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

The figure presents 2 horizontal lines l and k, with line l above line k. A third line, labeled j, runs from the bottom left and slants to the top right, intersecting both lines l and k. The angle above line l and to the left of line j is labeled a degrees. The angle above line k and to the right of line j is labeled 64 degrees. Note that the figure is not drawn to scale.

In the figure above, lines $l$ and k are parallel. What is the value of a ?

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Explanation

Choice C is correct. Since lines $l$ and k are parallel, corresponding angles formed by the intersection of line j with lines $l$ and k are congruent. Therefore, the angle with measure a° must be the supplement of the angle with measure 64°. The sum of two supplementary angles is 180°, so a = 180 – 64 = 116.

Choice A is incorrect and likely results from thinking the angle with measure a° is the complement of the angle with measure 64°. Choice B is incorrect and likely results from thinking the angle with measure a° is congruent to the angle with measure 64°. Choice D is incorrect and likely results from a conceptual or computational error.