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In the figure, angle ABE = angle ECD and angle EBD = angle ACE.  If angle BAC = 80 degrees and angle BEC = 100 degrees, then find obtuse angle BDC.

 

 Jan 8, 2020
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Let  angles  ABE and  ECD  = x

And let  angles EBD and ACE  = y

 

So  in   quadrilateral ABCE  angle BCE  = 360 - 100  = 260°

 

And in a quadrilateral, the sum of the interior angles = 360°

 

So  we have that     

 

80 + 260 + x + y  = 360

340 + x + y = 360

x + y = 20

 

And in quadrilateral   BECD  we have that

100 + x + y + (360 - angle BDC ) =  360

100 + 20  + 360 - angle BDC  = 360

120  - angle BDC  = 0

 

Angle BDC  =120°

 

 

cool cool cool

 Jan 8, 2020

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