Polígonos

Project ID: 
6000000005
Accepted: 
Tipo: 
Layout: 
Question: 
La figura muestra polígonos regulares. Asigna la medida de cada ángulo marcado:
Question 1 Image: 
Answer 1: 
$22.5^\circ $
Question 2 Image: 
Answer 2: 
$120^\circ $
Question 3 Image: 
Answer 3: 
$54^\circ $
Question 4 Image: 
Answer 4: 
$67.5^\circ $
Question 5 Image: 
Answer 5: 

$60^\circ $

Question 6 Image: 
Answer 6: 
$75^\circ $
Tex: 
% http://math4u.vsb.cz/ticket/32004 \NastavOD{6} \otazka{ \obrMsr{-1.3,1.35,-1.3,1.35}[3.5cm,] { \draw (0,0) circle (0.92); \foreach \i/\j in {1/A,2/B, 3/C, 4/D, 5/E, 6/F, 7/G,8/H} { \draw ({cos(-112.5+(\i-1)*(360.0/8))},{sin(-112.5+(\i-1)*(360.0/8))}) node {} coordinate (\j); \draw ({1.2*cos(-112.5+(\i-1)*(360.0/8))},{1.2*sin(-112.5+(\i-1)*(360.0/8))}) node {$\j$}; } \draw (A)--(B)--(C)--(D)--(E)--(F)--(G)--(H)--cycle; \draw[dashed] (A)--(E)--(B)--(F); \obrUhelB[10mm]{A}{E}[?]{B} \draw (0,0) node[left] {$S$}; }}{$22{,}5^\circ$} \otazka{\obrMsr{-1.3,1.35,-1.3,1.35}[3.5cm,] { \draw (0,0) circle (1); \foreach \i/\j in {1/A,2/B, 3/C, 4/D, 5/E, 6/F} { \draw ({cos(-210+(\i)*(360.0/6))},{sin(-210+(\i)*(360.0/6))}) node {} coordinate (\j); \draw ({1.2*cos(-210+(\i)*(360.0/6))},{1.2*sin(-210+(\i)*(360.0/6))}) node {$\j$}; } \draw (A)--(B)--(C)--(D)--(E)--(F)--(G)--(H)--cycle; \draw[dashed] (B)--(E); \draw[dashed] (C)--(F); \obrUhelB*[6mm]{C}{D}[?]{E} \draw (0,0) node[right] {$S$}; }}{$120^\circ$} \otazka{\obrMsr{-1.3,1.35,-1.3,1.35}[3.5cm,] { \draw (0,0) circle (1); \foreach \i/\j in {1/A,2/B, 3/C, 4/D, 5/E} { \draw ({cos(-126-72+(\i)*(360.0/5))},{sin(-126-72+(\i)*(360.0/5))}) node {} coordinate (\j); \draw ({1.2*cos(-126-72+(\i)*(360.0/5))},{1.2*sin(-126-72+(\i)*(360.0/5))}) node {$\j$}; } \draw (A)--(B)--(C)--(D)--(E)--cycle; \draw[dashed] (B)--(0,0); \draw[dashed] (A)--(0,0); \obrUhelB[6mm]{B}{A}[?]{0,0} \draw (0,0) node[above] {$S$}; }}{$54^\circ$} \otazka{\obrMsr{-1.3,1.35,-1.3,1.35}[3.5cm,] { \draw (0,0) circle (0.92); \foreach \i/\j in {1/A,2/B, 3/C, 4/D, 5/E, 6/F, 7/G,8/H} { \draw ({cos(-112.5+(\i-1)*(360.0/8))},{sin(-112.5+(\i-1)*(360.0/8))}) node {} coordinate (\j); \draw ({1.2*cos(-112.5+(\i-1)*(360.0/8))},{1.2*sin(-112.5+(\i-1)*(360.0/8))}) node {$\j$}; } \draw (A)--(B)--(C)--(D)--(E)--(F)--(G)--(H)--cycle; \draw[dashed] (A)--(E); \draw[dashed] (B)--(F); \obrUhelB[6mm]{B}{A}[?]{0,0} \draw (0,0) node[right] {$S$}; }}{$67{,}5^\circ$} \otazka{\obrMsr{-1.3,1.35,-1.3,1.35}[3.5cm,] { \draw (0,0) circle (1); \foreach \i/\j in {1/A,2/B, 3/C, 4/D, 5/E, 6/F, 7/G, 8/H, 9/I} { \draw ({cos(130+(\i)*(360.0/9))},{sin(130+(\i)*(360.0/9))}) node {} coordinate (\j); \draw ({1.2*cos(130+(\i)*(360.0/9))},{1.2*sin(130+(\i)*(360.0/9))}) node {$\j$}; } \draw (A)--(B)--(C)--(D)--(E)--(F)--(G)--(H)--(I)--cycle; \draw[] (B)--(E)--(H); \obrUhelB*[6mm]{B}{E}[?]{H} \draw (0,0) node[below] {$S$}; \obrKrizek{0,0}{}{} }}{$60^\circ$} \otazka{\obrMsr{-1.3,1.35,-1.3,1.35}[3.5cm,] { \draw (0,0) circle (1); \foreach \i/\j in {1/A,2/B, 3/C, 4/D, 5/E, 6/F, 7/G, 8/H, 9/I, 10/J, 11/K, 12/L} { \draw ({cos(150+(\i)*(360.0/12))},{sin(150+(\i)*(360.0/12))}) node {} coordinate (\j); \draw ({1.2*cos(150+(\i)*(360.0/12))},{1.2*sin(150+(\i)*(360.0/12))}) node {$\j$}; \draw[dashed] (0,0)--(\j); } \draw (A)--(B)--(C)--(D)--(E)--(F)--(G)--(H)--(I)--(J)--(K)--(L)--cycle; \obrUhelB*[5mm]{0,0}{H}[?]{I} }}{$75^\circ$} \def\preAnswers{\vspace*{-12pt}}