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we're asked to name an angle adjacent to angle bgd so angle bgd let's see if we can pick it out so here is B here is G and here is D right over here so angle bgd is this entire angle this entire angle right over here so when we talk about adjacent angles we're talking about an angle that has one of its rays in common so for example triangle a G B has one of the Rays in common as G be in common with angle bgd so we could say angle a G B a G B which could obviously also be called angle B G a B G a and a G B are both this angle right over here you could also go with angle F G B because that also has G B in common so you could go angle F G B which could also be written as angle B GF or you could go over here angle E G D shares rayji D in common so you could do this angle right over here angle e G D or you could go all the way out here angle F G D angle F G D these last two sharing Ray Gd in common so any one of these responses would be would be would satisfy the question of just naming an angle just naming one let's do this next one name an angle vertical - angle E G a angle E G a so this is this angle this is this angle right over here and the way you think about vertical angles is imagine two lines crossing so imagine two lines crossing just like this and it could literally be lines they're intersecting at a point this is forming this is forming four angles or you could imagine it's forming two sets of vertical angles so if this is the angle that you care about it's a vertical axis its vertical angle is the one on the opposite side of the intersection it's one of these angles that it is not adjacent - so it would be this angle right over here so going back to the question a vertical angle to angle EGA well if you imagine the intersection of line EB and line da then the non adjacent angle formed to angle EGA is angle D GB actually what we already highlighted in magenta right over here so this is angle D G B which could also be called angle B G D these are obviously both referring to this angle up here named an angle that forms a linear pair with angle D F G so I'm just in a new color angle D F G d/f vo - sorry DG f you always a should have G in the middle D gf so linear pair with angle D G F so that's this angle right over here so an angle that forms a linear pair will be an angle that is adjacent where the two outer rays combined will form a line so for example if you combine angle D G F which is this angle and angle D G C then they're two outer rays form this entire form this entire line right over here so we could say angle D G C angle D G C or if you look at angle D F G you could form a line this way if you take angle a G F so if you take this one then the outer rays will form this line so angle a G F would also work angle a G F let's do one more name a vertical angle to angle F G B F G B so this is f G B right over here you could imagine this angle is one of the four angles formed when C F let me highlight this when C that's hard to see when C F when C F is the last one so I can make a mess out of this that angle is formed when C F and E B intersect with each other intersect with each other and four angles are formed the one in question f G B these two angles that are adjacent to it it shares a common and then the vertical angle the one that sits on the opposite side so this angle this angle right over here which is angle EGC or you could also call it angle cge so angle C G E