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

In the figure shown, line $m$ is parallel to line $n$ . What is the value of $x$ ?

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Explanation

Choice D is correct. The sum of consecutive interior angles between two parallel lines and on the same side of the transversal is $180$ degrees. Since it's given that line $m$ is parallel to line $n$ , it follows that $x + 26 = 180$ . Subtracting $26$ from both sides of this equation yields $154$ . Therefore, the value of $x$ is $154$ .

Choice A is incorrect. This is half of the given angle measure.

Choice B is incorrect. This is the value of the given angle measure.

Choice C is incorrect. This is twice the value of the given angle measure.