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either of two angles whose sum is 180 degrees

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either of two angles whose sum is 90 degrees

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https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-angles/v/angles-at-the-intersection-of-two-lines

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http://study.com/academy/lesson/what-are-adjacent-angles-definition-examples.html

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Definition

Adjacent angles are two angles that have a common vertex and a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle. When we say common vertex and common side, we mean that the vertex point and the side are shared by the two angles. Here's an example of adjacent angles:

In this diagram, point A is the vertex of all of the angles shown. Angle DAJ and angle JAT are adjacent angles because the red ray AJ forms a side of each of those angles.

You can think of adjacent angles as two pizza slices next to each other in the box. The corners of the slices are both at the center of the box; that's where the vertex is. The cut where the slices were separated from one another is the side the angles share.

In the whole pizza, there are several other pairs of adjacent angles. Every angle can have two possible different angles adjacent to it, one attaching to each side of it. Using our pizza slices, if you have three slices of pizza, the middle piece has two pieces that are adjacent to it. Just remember that adjacent angles refers to two angles at a time.

Examples

Can you name two pairs of adjacent angles here?

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what are adjacent angles? - definition & examples - video & lesson transcript | study.com

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What Are Adjacent Angles? - Definition & Examples - Video & Lesson Transcript | Study.com

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Adjacent angles are two angles that have a common vertex and a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle. When we say common vertex and common side, we mean that the vertex point and the side are shared by the two angles.

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Angle bisector definition - Math Open Reference

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Definition of 'Angle Bisector' and a general discussion of bisection. Link to 'line bisector'

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The midpoint of a segment is a point that divides the segment into two congruent segments.