An adjacent angle linear pair is a pair of adjacent angles (angles sharing a common vertex and side) whose non-common sides form a straight line, and whose measures sum to 180 degrees.
To break it down further:
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Adjacent Angles: These are angles that are next to each other. They share a common vertex (corner point) and a common side (ray).
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Linear Pair: This means the two angles, in addition to being adjacent, also have the special property that their non-common sides form a straight line. Because a straight line forms an angle of 180 degrees, the measures of the two angles in a linear pair always add up to 180 degrees. These angles are supplementary.
Think of it like two slices of pie sitting next to each other that together form a half-circle. Each slice is an angle, and together they form a straight line (180 degrees).
Key Characteristics of an Adjacent Angle Linear Pair:
- Adjacent: They share a common vertex and a common side.
- Supplementary: Their measures add up to 180 degrees.
- Form a Straight Line: The non-common sides of the two angles create a straight line.
Example:
Imagine two angles, angle ABC and angle CBD, where B is the common vertex and BC is the common side. If angles ABC and CBD are adjacent and the rays BA and BD form a straight line, then angles ABC and CBD form a linear pair. Therefore, m∠ABC + m∠CBD = 180°.
