Project ID:
6000000005
Accepted:
Typ:
Layout:
Question:
Wielokąty foremne przedstawiono na rysunku poniżej. Przypisz miarę do każdego oznaczonego kata.
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}}