Углови - понављање градива
Решени задаци. Припрема за контролни задатак.
Задаци
Текст задатака објашњених у видео лекцији:
1.Повезати како је започето:
2. Претворити мере јединице:
| \[\left. a \right){3^\circ } = {\underline {} ^\prime }\] | \[\left. b \right)120'' = {\underline {} ^\prime }\] |
\[\left. c \right)20'' = {\underline {} ^{\prime \prime }}\] |
\[\left. d \right)36000'' = {\underline {} ^\circ }\] | \[\left. e \right){5^\circ } = {\underline {} ^\prime }\] |
|
\[\left. f \right)180'' = {\underline {} ^\prime }\] |
\[\left. g \right)10' = {\underline {} ^{\prime \prime }}\] |
\[\left. i \right)7200'' = {\underline {} ^\circ }\] | \[\left. j \right)6' = {\underline {} ^{\prime \prime }}\] | \[\left. k \right)360000'' = {\underline {} ^\circ }\] |
3. Дати су углови $\alpha = {167^\circ }34'42''$ и $\beta = {89^\circ }47'54''$. Израчунати следеће углове:
(а) $\alpha + \beta $
(б) $\alpha - \beta $
(в) $2\beta $
(г) $\alpha :3$
4.Дат је угао $\alpha = {57^\circ }32'$. Одредити меру њему:
(а) комплементног
(б) суплементног
(в) унакрестног угла.
5. Одредити мере трансверзалних углова $\alpha $ и $\beta $, ако је угао $\alpha $ већи од $\beta $:
(а) за ${46^\circ }$
(б) пет пута.
6. Одредити мере углова на сликама.
1.
2.
| \[\left. a \right){3^\circ } = {\underline {180} ^\prime }\] | \[\left. b \right)120'' = {\underline 2 ^\prime }\] |
\[\left. c \right)20'' = {\underline {1200} ^{\prime \prime }}\] |
\[\left. d \right)36000'' = {\underline {10} ^\circ }\] | \[\left. e \right){5^\circ } = {\underline {300} ^\prime }\] |
|
\[\left. f \right)180'' = {\underline 3 ^\prime }\] |
\[\left. g \right)10' = {\underline {600} ^{\prime \prime }}\] |
\[\left. i \right)7200'' = {\underline 2 ^\circ }\] | \[\left. j \right)6' = {\underline {360} ^{\prime \prime }}\] | \[\left. k \right)360000'' = {\underline {100} ^\circ }\] |
3. $\alpha = {167^\circ }34'42''$ и $\beta = {89^\circ }47'54''$
4.Угао $\alpha = {57^\circ }32'$
(а) комплементни:
$\alpha + \beta = {90^ \circ }$
${57^ \circ }32' + \beta = {90^ \circ }$
$\beta = {90^ \circ } - {57^ \circ }32'$
$\beta = {32^ \circ }28'$
(б) суплементни:
$\alpha + \beta = {180^ \circ }$
${57^ \circ }32' + \beta = {180^ \circ }$
$\beta = {180^ \circ } - {57^ \circ }32'$
$\beta = {122^ \circ }28'$
(в) унакрестни:
$\alpha = \beta $
$\beta = {57^\circ }32'$
5. Одредити мере трансверзалних углова $\alpha $ и $\beta $, ако је угао $\alpha $ већи од $\beta $:
(а) за ${46^\circ }$
\[\begin{gathered}
\alpha = \beta + {46^ \circ } \hfill \\
\alpha + \beta = {180^ \circ } \hfill \\
\beta + {46^ \circ } + \beta = {180^ \circ } \hfill \\
2\beta = {180^ \circ } - {46^ \circ } \hfill \\
2\beta = {134^ \circ } \hfill \\
\beta = {134^ \circ }:2 \hfill \\
\beta = {67^ \circ } \hfill \\
\alpha = {67^ \circ } + {46^ \circ } \hfill \\
\alpha = {113^ \circ } \hfill \\
\end{gathered} \]
(б) пет пута
\[\begin{gathered}
\alpha = 5\beta \hfill \\
\alpha + \beta = {180^ \circ } \hfill \\
5\beta + \beta = {180^ \circ } \hfill \\
6\beta = {180^ \circ } \hfill \\
\beta = {180^ \circ }:6 \hfill \\
\beta = {30^ \circ } \hfill \\
\alpha = 5 \cdot {30^ \circ } \hfill \\
\alpha = {150^ \circ } \hfill \\
\end{gathered} \]
6.
\[\begin{array}{*{20}{c}}
\begin{gathered}
\alpha = 2x \hfill \\
\beta = 3x \hfill \\
\alpha + \beta = {90^ \circ } \hfill \\
5x = {90^ \circ } \hfill \\
x = {90^ \circ }:5 \hfill \\
x = {18^ \circ } \hfill \\
\alpha = 2 \cdot {18^ \circ } \hfill \\
\alpha = {36^ \circ } \hfill \\
\beta = 5 \cdot {18^ \circ } \hfill \\
\beta = {54^ \circ } \hfill \\
\end{gathered} &{}&\begin{gathered}
\beta = 5\alpha \hfill \\
\alpha + 5\alpha = {180^ \circ } \hfill \\
5\alpha + \alpha = {180^ \circ } \hfill \\
6\alpha = {180^ \circ } \hfill \\
\alpha = {180^ \circ }:6 \hfill \\
\alpha = {30^ \circ } \hfill \\
\beta = 5 \cdot {30^ \circ } \hfill \\
\beta = {150^ \circ } \hfill \\
\hfill \\
\hfill \\
\end{gathered} &{}&\begin{gathered}
\beta = {54^ \circ } \hfill \\
{110^ \circ } + \alpha = {180^ \circ } \hfill \\
\alpha = {180^ \circ } - {110^ \circ } \hfill \\
\alpha = {70^ \circ } \hfill \\
\gamma = \alpha \hfill \\
\gamma = {70^ \circ } \hfill \\
\hfill \\
\hfill \\
\hfill \\
\hfill \\
\end{gathered}
\end{array}\]