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I'm solving some practice problems to prepare for a competitive exam . Here is one which I'm trying to do for some time but still haven't found a solution to :

"In the given figure , ∠ABC = 2∠ACB and AB=DC .Also , AD is the bisector of ∠BAC . Find ∠ABC "

Here is the drawing I made : Figure

Note that I want to find the numerical value of ∠ABC in degrees.
Since AB and DC are sides of different triangle , I don't know how to begin.
Also since none of the angles is known , how can I find the value of angle?
Please help.

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2 Answers 2

let angles *=y and o=x, AE=DE so base angles are equal. and by CPCT angle EDC will be 2y. So from triangle ADC y+y+2y+x=180 and from triangle ABC x+x+y+y+x=180, solving these x=36 and hence 2x=72 degrees

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Hi @SanjayJain. Welcome! Please use MathJax in future :) –  Shaun Mar 15 at 15:29
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Hint: Let $BE$ be the bisector of $\angle ABC$ and connect $E$ with $D$. In triangles $ABE$ and $DCE$ we have $\angle ABE = \angle DCE$, $AB=DC$ and $BE=CE$. Hence $AE=ED$.

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