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

The figure presents a triangle with a horizontal base. The left and right sides of the triangle are both extended past the top vertex of the triangle. The bottom left angle is labeled 70 degrees, and the bottom right angle is labeled 50 degrees. The angle above the left side of the triangle and below the extension of the right side of the triangle is labeled x degrees.

In the figure above, two sides of a triangle are extended. What is the value of x ?

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Explanation

Choice B is correct. The sum of the interior angles of a triangle is 180°. The measures of the two interior angles of the given triangle are shown. Therefore, the measure of the third interior angle is 180° – 70° – 50° = 60°. The angles of measures x° and 60° are supplementary, so their sum is 180°. Therefore, x = 180 – 60 = 120.

Choice A is incorrect and may be the result of misinterpreting x° as supplementary to 70°. Choice C is incorrect and may be the result of misinterpreting x° as supplementary to 50°. Choice D is incorrect and may be the result of a calculation error.