Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$ \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$?

share|cite|improve this question
up vote 2 down vote accepted

It is not possible to prove $\angle D = \angle C$. Here is a counterexample:

\begin{align} \angle B_1 & = 45^\circ \\ \angle B_2 & = 135^\circ \\ \angle C & = 135^\circ \\ \angle D & = 45^\circ \end{align}

share|cite|improve this answer

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 $90^\circ$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.