Which angles are alternate exterior angles to angle 11 formed …

Mathematics Questions

Parallel lines r and s are cut by two transversals, parallel lines t and u. Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16. Which angles are alternate exterior angles with angle 11?

Short Answer

Alternate exterior angles are pairs of angles located on opposite sides of a transversal that intersects two parallel lines, and they are congruent. To determine these angles, identify the transversal and look for angles outside the parallel lines; for example, angle 13 and angle 5 are alternate exterior angles relative to angle 11.

Step-by-Step Solution

Step 1: Understand the Definition

To identify alternate exterior angles, it is crucial to first understand their definition. Alternate exterior angles are the pairs of angles that lie on opposite sides of a transversal intersecting two parallel lines. These angles are found outside the parallel lines and are congruent.

Step 2: Identify the Parallel Lines and Transversal

In the given situation, we have two sets of parallel lines: r is parallel to s, and t is parallel to u. By identifying the transversal that intersects these parallel lines, we can determine which angles are alternate exterior angles. Look for angles that are on opposite sides of this transversal.

Step 3: Locate the Alternate Exterior Angles

Based on the figure provided, we can identify the alternate exterior angles related to angle 11. Specifically, angle 13 and angle 5 are located on the exterior sides of the parallel lines and on opposite sides of the transversal. Therefore, these angles confirm the pairs of alternate exterior angles formed in this scenario.

Related Concepts

Alternate Exterior Angles

Angles that lie on opposite sides of a transversal intersecting two parallel lines, found outside the parallel lines, and are congruent

Transversal

A line that intersects two or more lines at different points

Parallel Lines

Lines in a plane that are equidistant from each other and never intersect.

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