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April 10th, 2015, 07:18 PM   #1
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Question 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.
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April 10th, 2015, 08:33 PM   #2
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Hello, Avlis Odraude!

Welcome aboard!


Quote:
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














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April 10th, 2015, 09:27 PM   #3
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$\displaystyle \angle{ABC}=\angle{ACB}=y$

$\displaystyle \angle{ADE}=\angle{AED}=x$

$\displaystyle 180-2x=180-20-2y=160-2y\implies x=10+y$

$\displaystyle \angle{DEC}=180-x=180-10-y,\angle{DCE}=y,\angle{EDC}=a$

$\displaystyle 180-10-y+y+a=180\implies a=10^{\circ}$
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