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Углови – понављање градива

Задаци

Текст задатака објашњених у видео лекцији:

1.Повезати како је започето:

108

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.

530 png

 

 

1.

528 png

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 $\beta  = {89^\circ }47'54''$

529 png

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. 

530 png

\[\begin{array}{*{20}{c}}
\begin{gathered}
\alpha = 2x \hfill \\
\beta = 3x \hfill \\
\alpha + \beta = {90^ \circ } \hfill \\
5x = {90^ \circ } \hfill \\
x = {90^ \circ }:5 \hfill \\
x = {18^ \circ } \hfill \\
\alpha = 2 \cdot {18^ \circ } \hfill \\
\alpha = {36^ \circ } \hfill \\
\beta = 5 \cdot {18^ \circ } \hfill \\
\beta = {54^ \circ } \hfill \\
\end{gathered} &{}&\begin{gathered}
\beta = 5\alpha \hfill \\
\alpha + 5\alpha = {180^ \circ } \hfill \\
5\alpha + \alpha = {180^ \circ } \hfill \\
6\alpha = {180^ \circ } \hfill \\
\alpha = {180^ \circ }:6 \hfill \\
\alpha = {30^ \circ } \hfill \\
\beta = 5 \cdot {30^ \circ } \hfill \\
\beta = {150^ \circ } \hfill \\
\hfill \\
\hfill \\
\end{gathered} &{}&\begin{gathered}
\beta = {54^ \circ } \hfill \\
{110^ \circ } + \alpha = {180^ \circ } \hfill \\
\alpha = {180^ \circ } - {110^ \circ } \hfill \\
\alpha = {70^ \circ } \hfill \\
\gamma = \alpha \hfill \\
\gamma = {70^ \circ } \hfill \\
\hfill \\
\hfill \\
\hfill \\
\hfill \\
\end{gathered}
\end{array}\]

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