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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 $k$ intersects both lines. Which of the following statements is true?

The value of $x$ is less than $145$ .

The value of $x$ is greater than $145$ .

The value of $x$ is equal to $145$ .

The value of $x$ cannot be determined.

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Explanation

Choice C is correct. Vertical angles, or angles that are opposite each other when two lines intersect, are congruent. It’s given that line $k$ intersects line $n$ . Based on the figure, the angle with measure $x °$ and the angle with measure $145 degree$ are vertical angles. Therefore, the value of $x$ is equal to $145$ .

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 D is incorrect and may result from conceptual or calculation errors.