\begin{exercice}
On considère un cube $ABCDEFGH$ d'arête 1. Soit $I$ le centre de la face $EFGH$ et $J$ celui de la face $ABFE$.
\begin{center}
 	\def \dx {-0.4}
 	\def \r {0.3}
	\begin{tikzpicture}[general, scale=2]
	%points
	\coordinate (A) at (0,0); \draw (A) node[left] {$A$};
	\coordinate (B) at (\dx,-0.5); \draw (B) node[below left] {$B$};
	\coordinate (C) at (1+\dx,-0.5); \draw (C) node[below] {$C$};
	\coordinate (D) at (1,0); \draw (D) node[right] {$D$};
	\coordinate (E) at (0,1); \draw (E) node[above left] {$E$};
	\coordinate (F) at (\dx,0.5); \draw (F) node[left] {$F$};
	\coordinate (G) at (1+\dx,0.5); \draw (G) node[right] {$G$};
	\coordinate (H) at (1,1); \draw (H) node[above right] {$H$};
	\coordinate (I) at ({(1+\dx)/2},0.75); \draw (I) node[above] {$I$};
	\coordinate (J) at (\dx/2,0.25); \draw (J) node[left] {$J$};
	%arêtes
	\draw (F)--(B)--(C)--(D)--(H)--(G)--(C); \draw (G)--(F)--(E)--(H);
	\draw[dashed] (A)--(B); \draw[dashed] (A)--(D); \draw[dashed] (A)--(E);
	%I et J
	\draw[thin] (E)--(G); \draw[thin] (F)--(H);
	\draw[thin, dashed] (E)--(B); \draw[thin, dashed] (F)--(A);
	%(JI) et (JD)
	\draw[dashed, color=C1] (D)--(J)--(I);
	%angle
	\fill[color=A1,opacity=0.3,domain=-11:44] (J)
						--plot ({\dx/2+\r*cos(\x)}, {0.25+\r*sin(\x)})
						--cycle;
	\end{tikzpicture}
\end{center}
En se plaçant dans un repère orthonormé bien choisi, calculer, au degré près, une mesure de l'angle $\widehat{IJD}$.
\end{exercice}

