# Help with a logic question

$\angle B_1 + \angle B_2 = 180^\circ$

$\angle C + \angle B_1 = 180^\circ$

$\angle D + \angle B_2 = 180^\circ$

Can I prove with these 3 statements that:

$\angle D = \angle C$?

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It is not possible to prove $\angle D = \angle C$. Here is a counterexample:
Rearranging each of the first two equations gives $\angle B_2 = 180^\circ - \angle B_1$ and $\angle C = 180^\circ - \angle B_1$ respectively, and so $\angle B_2 = \angle C$. Putting this into the third equation, we have $\angle D + \angle C = 180^\circ$. This does not imply that $\angle D = \angle C$, unless both are equal to $90^\circ$.