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

The figure presents a triangle. The bottom side is horizontal, the left side slants upward and slightly to the left, and the right side slants downward and to the right. The bottom left angle of the triangle measures 2 b degrees. The top angle of the triangle measures 31 degrees. The bottom right angle of the triangle measures a, degrees.

In the triangle above, $a, equals 45$ . What is the value of b ?

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Explanation

Choice A is correct. The sum of the measures of the three interior angles of a triangle is 180°. Therefore, $31 plus 2 b, plus a, equals 180$ . Since it’s given that $a, equals 45$ , it follows that $31 plus 2 b, plus 45, equals 180$ , or $2 b equals 104$ . Dividing both sides of this equation by 2 yields $b equals 52$ .

Choice B is incorrect and may result from a calculation error. Choice C is incorrect. This is the value of $a, plus 31$ . Choice D is incorrect. This is the value of $2 b$ .