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Geometry Problem I've been stuck on

 

https://docs.google.com/drawings/d/17RPrpkiNBO7xbTA6-UGuHT1juDVxpcU__cWdNXM9ocU/edit?usp=sharing

 

△AEB and △DEC are similar. Find x + y

 Mar 11, 2024
 #1
avatar+128794 
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If AEB similar to DEC, then angle  EDC  = angle EAB  and angle ECD = angle EBA

 

Then  the lines  through AB and CD are parallel because transversals DA and CB form equal opposite interor angles

 

Angles ECD + EDC  = 180 - angle CED =    180 - 80  =  100    

The supplemental angle to CDB =  111     call this angle D'

The suppplemental angle to ACD =  114     call this angle C'

 

So

 

C' + x + ECD  + EDC  + y + D'  =  360

 

C' + D' + ( ECD + EDC)  + x + y =  360

 

114 + 111 + (100) + x + y   =  360

 

325 + x + y =  360

 

x + y =  360 - 325  =   35

 

cool cool cool

 Mar 11, 2024

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