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

In the figure, line $m$ is parallel to line $n$ , and line $t$ intersects both lines. What is the value of $x$ ?

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Explanation

Choice D is correct. It’s given that line $m$ is parallel to line $n$ , and line $t$ intersects both lines. It follows that line $t$ is a transversal. When two lines are parallel and intersected by a transversal, exterior angles on the same side of the transversal are supplementary. Thus, $x + 33 = 180$ . Subtracting $33$ from both sides of this equation yields $x equals 147$ . Therefore, the value of $x$ is $147$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.