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In geometry, us give different names come different varieties of angles relying on the measure of the given angle: best angles, nearby supplementary angles, vertical angles. However how do we understand which is which?

Let’s start with the basics.

You are watching: Which angles are adjacent angles?

If the measure up of the edge is specifically 90 degrees, it’s known as a ideal angle. If an edge is less than 90 degrees, it’s an acute angle. An angle greater than 90 levels is an obtuse angle. If the measure of an angle is same to 180 degrees, it’s known as a right angle.

There are additionally names given to pairs the angles.

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Vertical angles, or the opposite angles, are the 2 angles straight opposite each other when two right lines overcome (Figure 1).

Complementary angles room two angle that add to 90 levels (Figure 2).

Supplementary angles are two angles that include up come 180 degrees (Figure 3).

Adjacent angle vs. Nonadjacent Angles

Angles are adjacent when lock share a common side and a common vertex.

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Angles 1 and also 2 are nonadjacent, while angles 3 and also 4 room — lock share a typical side and also vertex.

Adjacent Supplementary angles Defined

Now the we understand the interpretations of surrounding and nonadjacent angles, we can see that surrounding supplementary angles are two angle that re-publishing a side and vertex and add up come 180 degrees.

Using this definition, look in ~ the diagram listed below to check out which angle are adjacent supplementary.

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Angles ABC and ABD are nearby because castle share line segment abdominal and vertex B.

Angles EFG and also HIJ space not nearby because they nothing share any kind of common side.

However, the angle procedures in both bag of supplementary angles (ABC and ABD, and EFG and also HIJ) still equal 180 degrees.

To review, that means EFG and HIJ are supplementary angles. However, just ABC and also ABD are surrounding supplementary angles.

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Recognizing surrounding Supplementary Angles

To recap, adjacent supplementary angle don’t simply share a side and also vertex but they also include up come 180 degrees. These angles commonly show up in geometry proofs, so if you’re not sure, look because that a straight line intersected by an additional line segment with the two angles share a usual side and also vertex.