Hey, this is an English text. I want you to translate it into the Tunisian dialect. Please follow these steps:
1. Translate step by step and highlight differences between Tunisian dialect and Modern Standard Arabic.
2. Highlight sections you are confident translating into the Tunisian dialect.
Translate this text into the Tunisian dialect, focusing on capturing the essence of the language nuances:

Q: Missing Delimiter (.inserted) error. How do I fix this? \begin{proof} We are given that there exists a quadrilateral $ABCD$ on a sphere. Let us create a line segment $AC$ that divides our quadrilateral into two triangles. Thus, $\angle{A}$ and $\angle{C}$ have been divided by our line segment $AC$. Let the portion of $\angle{A}$ and $\angle{C}$ on the same side of $AC$ as $B$ be called $\angle{A_1}$ and $\angle{C_1}$. Also, Let the portion of $\angle{A}$ and $\angle{C}$ on the same side of $AC$ as $D$ be called $\angle{A_2}$ and $\angle{C_2}$. Therefore, \begin{align*} \left|ABCD|\right &=\left|\Delta{ABC}|+|\Delta{ACD}|\right\\ \ &= \left p^2(\angle{A_1}+\angle{B}+\angle{C_1}-\pi)+p^2(\angle{A_2}+\angle{C_2}+\angle{D}-\pi)\right\\ \ &= \left p^2(\angle{A_1}+\angle{B}+\angle{C_1}+\angle{A_2}+\angle{C_2}+\angle{D}-2\pi)\right. \end{align*} However, \[\angle{A_1}+\angle{A_2}=\angle{A}\] and \[\angle{C_1}+\angle{C_2}=\angle{C}\] \[\left|ABCD|\right=\left p^2(\angle{A}+\angle{B}+\angle{C}+\angle{D}-2\pi)}\right\]. To generalize furthur the area of any $n$-sided polygon on the sphere is as follows, \[\left{Area of an N-sided Polygon}\right=\left(sum of the angles-(n-2)\pi\right\] \end{proof} This is code that is producing the missing delimiter error, it says the problem is occurring somewhere with the align environment. Anyone have suggestions? A: the problem here is how the \left and \right commands are used. each of these commands always requires either an actual delimiter -- parenthesis, bracket, etc. -- or a "placeholder", namely a period. in the first line of the alignment, the \right is placed after the |; it should be before. so at the beginning of the second and third lines (and perhaps elsewhere, i didn't check), \left is not followed by any delimiter, it's not clear what delimiter is to be "matched". perhaps the opening parenthesis after \p^2? here is the reformulated display: \begin{align*} \left|ABCD\right| &=\left|\Delta{ABC}\right|+\left|\Delta{ACD}\right|\\ \ &= p^2\left(\angle{A_1}+\angle{B}+\angle{C_1}-\pi)+p^2(\angle{A_2} +\angle{C_2}+\angle{D}-\pi\right)\\ \ &= p^2\left(\angle{A_1}+\angle{B}+\angle{C_1}+\angle{A_2} +\angle{C_2}+\angle{D}-2\pi\right). \end{align*} actually, since most of the symbols between the delimiters aren't taller than the normal text, \left and \right aren't really needed. in the paragraph following the align*, i think you're confusing \[ and \] with the actual square brackets. the "escaped" forms indicate the beginning and end of a one-line math display. no backslashes should be used if an actual bracket is intended. however, a typeset brace must be entered preceded by a backslash. and within a math environment, normal text (the "Area of ...") needs to be so indicated, by \text{...}, and within that string, any small math expressions need to be returned to math mode by $...$. here is that paragraph reformulated: However, [\angle{A_1}+\angle{A_2}=\angle{A}] and [\angle{C_1}+\angle{C_2}=\angle{C}] [\left|ABCD\right|= p^2\left(\angle{A}+\angle{B}+\angle{C} +\angle{D}-2\pi\right)}]. To generalize further the area of any $n$-sided polygon on the sphere is as follows, \[\left\{\text{Area of an $N$-sided Polygon}\right\} =\left\{\text{sum of the angles $-(n-2)\pi$}\right\}\] i may have misunderstood your intent in the paragraph following the display; if you really did intend these bracketed expressions to be displayed, then instead of coding each one as a separate display, you should use the gather* environment. you don't say what document class or theorem package you are using. however, in any event, you shouldn't ever leave a blank line before \end{proof} -- that will guarantee that the "tombstone" is always set on a line by itself. also, if you are using amsthm, you can insert \qedhere before