Understanding Adjacent Angles: Definition, Properties, and Examples

adjacent angles

two angles that have a common vertex and a common side

Adjacent angles are two angles that share a common vertex and a common side. In other words, they are two angles that are next to each other and share a common endpoint and a side.

For example, in the figure below, ∠ABC and ∠CBD are adjacent angles because they share the common vertex point B and the common side BC.

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A
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B—–C
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D
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One important property of adjacent angles is that their sum is equal to the measure of the larger angle that contains both of them. This is known as the Angle Addition Postulate, and can be expressed mathematically as follows:

If ∠ABC and ∠CBD are adjacent angles, then:

∠ABC + ∠CBD = ∠ABD

This property is useful in solving problems involving adjacent angles, such as finding the measure of an unknown angle when its adjacent angles are given.

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