## What are surrounding angles?

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

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

**Nonadjacent angles**

Nonadjacent angles might or may not re-superstructure a common vertex, however they carry out not have any type of rays in common.

In this diagram, angles ???1??? and ???2??? are not adjacent, even though castle share vertex ???W???, because they execute not share a common 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 usual vertex and also a typical ray.

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

???angle DWA??? is nearby to ???angle DWC???: they share vertex ???W??? and ray ???vecWD???.

???angle DWC??? is adjacent to ???angle CWB???; they share vertex ???W??? and ray ???vecWC???.

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

Notice that you deserve to tell indigenous the way the angles space written which ray they share. For example,

???angle CWB??? is surrounding to ???angle AWB???; lock share crest ???W??? and ray ???vecWB???. Since ???angle AWB??? and ???angle CWB??? both have actually the letter ???W??? and also ???B??? from ray ???vecWB???.

Let’s see about how come identify possible adjacent angle without a diagram.

Nonadjacent angles might or may not share a usual vertex, but they do not have any type of rays in common.

**Example**

All the the edge pairs room from the very same diagram. Classify each pair as surrounding or non-adjacent.

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

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

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

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

Remember that surrounding angles have actually the exact same vertex and also share one typical ray. An edge name always has the crest in the middle. You deserve to then use the angle name to find the rays the make the angle.

Let’s look at each angle pair.

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

B. ???angle XYZ??? and ???angle ZYX???. Both the these angles share crest ???Y???. Currently we have to look because that one typical ray. ???angle XYZ??? has rays ???vecYX??? and ???vecYZ??? and also ???angle ZYX??? has actually rays ???vecYZ??? and ???vecYX???, which means that both angle share rays ???vecYX??? and also ???vecYZ???. Therefore, ???angle XYZ??? and also ???angle ZYX??? are various ways to name the exact same angle.

C. ???angle LMN??? and ???angle MNP???. ???angle LMN??? has actually vertex ???M??? and ???angle MNP??? has actually vertex ???N???, so these angles carry out not re-superstructure a vertex and they room nonadjacent.

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D. ???angle CED??? and also ???angle CEP???. Both the these angles share peak ???E???. Now we must look because that one typical ray. ???angle CED??? has rays ???vecEC??? and also ???vecED??? and also ???angle CEP??? has actually rays ???vecEC??? and also ???vecEP???, which method that both angles share ray ???vecEC???. Therefore, ???angle CED??? and ???angle CEP??? are surrounding angles.