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Find x! Thank you!

 May 5, 2020
 #1
avatar+111326 
+1

Note that triangles  BFG  and  DJI  are isosceles

 

angle BFG  =angle BGF  =  [180 - 36] /2  =  144/2  = 72°

 

angle DJI  = angle DIJ  = [ 180 - 39]/ 2  = 70.5°

 

angles EGF  and DFG   are supplemental to angles  BFG and BGF....so   they measure  108- 72  = 108”  

 

Likewise  angles FJI  and CIJ  are sumpplementary to  angles DJI and DIJ....so  they measure 180 - 70.5  = 109.5°

 

And  in pentagon FGHOJ  the sum of its interior angles  = 540°

 

Therefore

 

EGF  + DFG  + FJI + CIJ  + GHI   = 540

 

108 + 108  +  109.5  + 109.5  + GHI  =540

 

435  + GHI   = 540

 

GHI  = 540  - 435  =  105°

 

But angle EHI  is supplemental  to GHI  so its measure    =  180 - 105  =  75°  = x 

 

 

 

cool cool cool

 May 5, 2020

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