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Find angle DAC + angle EBD + angle ACE + angle BDA + angle CEB.

 

 Dec 31, 2019
 #1
avatar+2551 
+2

Click here for the solution.

 

Its a great video.

 

Just watch from the beginning to 2:30.

 

 

In two minutes and 30 seconds you can solve this problem easily!

 Dec 31, 2019
 #2
avatar+106519 
+2

Let DAC  = A      EBD  = B     ACE  = C    BDA  = D     CEB   = E

 

Starting a the top left and  moving clock-wise, call the  interior angles  of the  interior  irregular pentagon 

  F , G, H, I , J 

 

The sum of these interior angles =   540°

 

And the sum of the angles of the five triangles abutting  this irregular pentagon =  5 * 180  = 900°

 

So.....the    base  angles  on the sides of the  triangles  abutting this irregular pentagon  lead to this equation

 

2(180 - F) + 2(180 - G)  + 2(180 - H)  + 2 (180 - I) + 2(180 - J)  +  A + B + C + D + E  = 900

 

Simplify

 

1800 -  2 ( F + G + H + I + J)  +  A + B + C + D + E  =  900

 

1800 - 2(540)  +  A + B + C + D + E  = 900

 

1800 - 1080  + A + B + C + D + E =  900

 

720  + A + B + C + D + E   = 900

 

A + B + C + D + E   =  900  -720   =   180°

 

 

 

cool cool cool

 Dec 31, 2019

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