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April 10th, 2015, 07:18 PM  #1 
Newbie Joined: Sep 2014 From: Brazil Posts: 1 Thanks: 0  Problem with isosceles triangles
Hi; this is my first post. I'm puzzling my brain with this dumb problem, without success . Here's the question: one big isosceles triangle (AB=AC) and another isosceles, inside the big one (AD=AE) – see the representation below. The angle ∠BAD is 20º. What the value of angle ∠EDC? https://imageshack.us/i/exbKvtpLj The alternatives for the problem are a) 5º b) 10º c) 15º d) 20º e) 25º I tried using the exterior angle theorem, but I got 20º; then I used ruler, compass and protractor and... 10º. What the... Hoping help... Last edited by Avlis Odraude; April 10th, 2015 at 07:35 PM. 
April 10th, 2015, 08:33 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, Avlis Odraude! Welcome aboard! Quote:
 
April 10th, 2015, 09:27 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond 
$\displaystyle \angle{ABC}=\angle{ACB}=y$ $\displaystyle \angle{ADE}=\angle{AED}=x$ $\displaystyle 1802x=180202y=1602y\implies x=10+y$ $\displaystyle \angle{DEC}=180x=18010y,\angle{DCE}=y,\angle{EDC}=a$ $\displaystyle 18010y+y+a=180\implies a=10^{\circ}$ 

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