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6. Name each angle pair as corresponding, alternate interior, alternate exterior, consecutive int consecutive exterior, or no relationship. Identify the transversal that connects each angle pai a) \( \angle 4 \) and \( \angle 10 \) \( \begin{array}{ll}\text { b) } \angle 8 \text { and } \angle 11 \\ \text { c) } \angle 1 \text { and } \angle 4 & \text {; Transseessats } \\ \text { d) } \angle 2 \text { and } \angle 12 & \text {; Transversal: } \\ \text { e) } \angle 5 \text { and } \angle 7 & \text {; Transversal: } \\ \text { f) } \angle 2 \text { and } \angle 13\end{array} \)

Ask by Gross Adkins. in the United States
Mar 09,2025

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a) \(\angle 4\) and \(\angle 10\) are **alternate exterior angles** with the common transversal.

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**a) \(\angle 4\) and \(\angle 10\)** These two angles lie on opposite sides of a transversal and are “outside” the two parallel lines. In other words, they are an  \[ \textbf{alternate exterior angles.} \] Their common transversal is the line that crosses both parallel lines so that the vertex of \(\angle 4\) (at one intersection) and the vertex of \(\angle 10\) (at the other intersection) lie on it. --- **

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a) \( \angle 4 \) and \( \angle 10 \) are alternate exterior angles. The transversal connecting them is the line that intersects the two parallel lines above \( \angle 4 \) and below \( \angle 10 \). b) \( \angle 8 \) and \( \angle 11 \) are alternate interior angles. The transversal here runs between the two parallel lines intersecting at \( \angle 8 \) and \( \angle 11 \). c) \( \angle 1 \) and \( \angle 4 \) are corresponding angles. The transversal that connects these angles travels across one of the parallel lines from \( \angle 1 \) to \( \angle 4 \). d) \( \angle 2 \) and \( \angle 12 \) are consecutive interior angles. Their transversal is the one that runs between these two angles along the interior of the parallel lines. e) \( \angle 5 \) and \( \angle 7 \) are corresponding angles. They are connected by the transversal that crosses from \( \angle 5 \) to \( \angle 7 \) along the same line. f) \( \angle 2 \) and \( \angle 13 \) have no relationship as angle pairs. The transversal connecting angles from the two parallel lines does not link them directly.

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