## What are surrounding angles?

In this lesson fine look at how to identify nearby angles in a diagram and how to type angle names.

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In this diagram, angle ???1??? and also ???2??? are surrounding because lock share peak ???G??? and also ray ???vecGB???.

**Nonadjacent angles**

Nonadjacent angles may or may not re-publishing a usual vertex, however they do not have any type of rays in common.

In this diagram, angle ???1??? and ???2??? space not adjacent, even though they share vertex ???W???, because they perform not share a typical ray.

## Finding bag of nearby angles with and also without a diagram

**Example**

List the bag of nearby angles in the diagram.

Adjacent angle share a typical vertex and a usual ray.

???angle DWA??? is surrounding to ???angle AWB???; castle share crest ???W??? and ray ???vecWA???.

???angle DWA??? is adjacent to ???angle DWC???: lock share peak ???W??? and also ray ???vecWD???.

???angle DWC??? is nearby to ???angle CWB???; lock share peak ???W??? and ray ???vecWC???.

???angle CWB??? is adjacent to ???angle AWB???; castle share crest ???W??? and also ray ???vecWB???.

Notice the you have the right to tell from the method the angles room written which ray they share. For example,

???angle CWB??? is adjacent to ???angle AWB???; castle share crest ???W??? and ray ???vecWB???. Since ???angle AWB??? and also ???angle CWB??? both have the letters ???W??? and also ???B??? from beam ???vecWB???.

Let’s see around how come identify feasible adjacent angle without a diagram.

Nonadjacent angles may or may not share a typical vertex, however they execute not have any kind of rays in common.

**Example**

All the the angle pairs are from the same diagram. Classify each pair as adjacent or non-adjacent.

A. ???angle ABC??? and also ???angle CBD???

B. ???angle XYZ??? and also ???angle ZYX???

C. ???angle LMN??? and also ???angle MNP???

D. ???angle CED??? and ???angle CEP???

Remember that adjacent angles have the exact same vertex and share one typical ray. An edge name always has the vertex in the middle. You have the right to then use the angle name to discover the rays the make the angle.

Let’s look at at every angle pair.

A. ???angle ABC??? and ???angle CBD???. Both of these angles share crest ???B???. Now we need to look because that one common ray. ???angle ABC??? has rays ???vecBA??? and ???vecBC??? and ???angle CBD??? has actually rays ???vecBC??? and also ???vecBD???, which method that both angles share ray ???vecBC???. Therefore, ???angle ABC??? and also ???angle CBD??? are adjacent angles.

B. ???angle XYZ??? and ???angle ZYX???. Both of these angle share peak ???Y???. Currently we must look because that one usual ray. ???angle XYZ??? has actually rays ???vecYX??? and ???vecYZ??? and ???angle ZYX??? has actually rays ???vecYZ??? and also ???vecYX???, which means that both angles share light ray ???vecYX??? and ???vecYZ???. Therefore, ???angle XYZ??? and also ???angle ZYX??? are different ways to surname the exact same angle.

C. ???angle LMN??? and also ???angle MNP???. ???angle LMN??? has actually vertex ???M??? and ???angle MNP??? has actually vertex ???N???, so this angles do not re-superstructure a vertex and they are nonadjacent.

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D. ???angle CED??? and ???angle CEP???. Both of these angles share vertex ???E???. Now we need to look for one typical ray. ???angle CED??? has rays ???vecEC??? and also ???vecED??? and ???angle CEP??? has actually rays ???vecEC??? and ???vecEP???, which method that both angle share beam ???vecEC???. Therefore, ???angle CED??? and also ???angle CEP??? are nearby angles.