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I don't know how to prove or disprove the following problem: How to construct triangle if elements $a$, $b$, $\beta-\gamma$ are given? Is it constructible (if not, how to prove it)? Any help is welcome.

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What are $\beta$ and $\gamma$? – hjpotter92 May 30 '13 at 21:32
Angles at points B and C of triangle ABC – alans May 30 '13 at 22:20
Can you edit your question to explain more clearly what you mean by constructible. Do you mean with straightedge and compass? – Sammy Black May 30 '13 at 22:32
Yes, with straightedge and compass. – alans May 30 '13 at 22:34

I don't think that such a triangle can be constructed. A triangle construction needs 3 values known. These three values should be valid Congruence rule (such as SAS, SSS, ASA etc.).

Here, we are given 2 edges and difference of angles opposite to those sides. The two edges are 2 values and for third, we have no usable means to deduce. Just one relation between two angles is not enough.

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with $a,\angle B,C$ you can construct a triangle.but the extra b may cause conflict unless you ignore it. or you can use $a,b , \angle C$ to construct a triangle.but you have to omit $\angle B$.

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