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

In the figure shown, line $l$ intersects lines $j$ and $k$ . Which additional piece of information is sufficient to prove that lines $j$ and $k$ are parallel?

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Explanation

Choice A is correct. In the figure shown, lines $j$ and $k$ are parallel if and only if a pair of corresponding angles are congruent. It's given that one angle has a measure of $40 degree$ and that the corresponding angle has a measure of $w °$ . Therefore, $w equals 40$ is sufficient to prove that lines $j$ and $k$ are parallel.

Choice B is incorrect. The angle measuring $x °$ and the angle measuring $40 degree$ are alternate interior angles. Thus, if lines $j$ and $k$ are parallel, $x$ is equal to $40$ , not $140$ .

Choice C is incorrect. The angle measuring $y °$ and the angle measuring $40 degree$ are vertical angles. Thus, $y equals 40$ , whether lines $j$ and $k$ are parallel or not.

Choice D is incorrect. The angle measuring $z °$ is supplementary to the angle measuring $40 degree$ . Thus, $z = 180 - 40$ , or $z equals 140$ , whether lines $j$ and $k$ are parallel or not.