Consider an \(\color{pink}{isosceles}\) \(\color{purple}{\Delta ABC}\), with \(\color{green}{\angle A=20^{\circ}}\), and the other two angles being equal. \(D\) and \(E\) are points on \(\overline{AC}\) and \(\overline{AB}\) respectively, such that \(\color{orange}{\angle DBC=50^{\circ}}\) and \(\color{blue}{\angle ECB=60^{\circ}}\). Determine the magnitude of \(\angle DEC\) in degrees.

**Note:-** This question is not mine in any way whatsoever. It is a quite popular problem, and I could not find the exact source, and will be eagerly waiting for the same. Protractor users will be prosecuted.

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