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

The figure presents 5 lines labeled j, k, l, m, and n. Lines m and n are horizontal and line m lies above line n. Line j is slanted downward and to the right, and line k is slanted upward and to the right. Lines j, k, and top horizontal line m intersect, forming six angles. The angle below line m and to the left of line k and the angle below line m and to the right of line j are both labeled, a, degrees. Line k intersects the bottom horizontal line n, forming four angles. The angle above line n and to the left of line k is labeled 130 degrees. Line l is vertical and intersects lines m and n on the right side of the figure. Line j, line l, and the bottom horizontal line n intersect, forming six angles. The angle, above line n, to the left of vertical line l, and to the right of line j is labeled b degrees. There is a right angle symbol at an angle formed by horizontal line m and vertical line l.

In the figure above, lines m and n are parallel. What is the value of b ?

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Explanation

Choice A is correct. Given that lines m and n are parallel, the angle marked 130° must be supplementary to the leftmost angle marked a° because they are same-side interior angles. Therefore, 130° + a° = 180°, which yields a = 50°. Lines $l$ and m intersect at a right angle, so lines j, $l$ , and m form a right triangle where the two acute angles are a° and b°. The acute angles of a right triangle are complementary, so a° + b° = 90°, which yields 50° + b° = 90°, and b = 40.

Choice B is incorrect. This is the value of a, not b. Choice C is incorrect and may be the result of dividing 130° by 2. Choice D is incorrect and may be the result of multiplying b by 2.