Clockwise from top left, the 3 lines are labeled t, m, and n. Line t intersects both line m and

Question

Clockwise from top left, the 3 lines are labeled t, m, and n.
Line t intersects both line m and line n.
At the intersection of line t and line m, 1 angle is labeled clockwise from top left as follows:
- Bottom left: 134/li>
At the intersection of line t and line n, 1 angle is labeled clockwise from top left as follows:
- Bottom left: w/li>
A note indies the figure is not drawn to scale.

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

Accepted Answer

Choice D is correct. It's given that lines m and n are parallel. Since line t intersects both lines m and n , it's a transversal. The angles in the figure marked as 134 &#176; and w &#176; are on the same side of the transversal, where one is an interior angle with line m as a side, and the other is an exterior angle with line n as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that w &#176; = 134 &#176; . Therefore, the value of w is 134 . 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.

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