Question

Answer 1-10

all Answers must have Solution ​

Answer 1

A. Find the number of sides of a polygon, The sum of whose interior angle is:

1. 1260°

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm 1260 \degree= 180 \degree * \: (n - 2) \\\rm (1260 \degree)/(180 \degree) = (180 \degree(n - 2))/(180 \degree) \\ \rm 7 = n - 2 \\ \rm n = 7 + 2 \\ \rm n = 9\end{array}\end{gathered} \end{gathered}`

2. 1620°

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm 1620 \degree= 180 \degree * \: (n - 2) \\\rm (1620 \degree)/(180 \degree) = (180 \degree(n - 2))/(180 \degree) \\ \rm 9 = n - 2 \\ \rm n = 9 + 2 \\ \rm n = 11\end{array}\end{gathered} \end{gathered}`

3. 1980°

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm 1980 \degree= 180 \degree * \: (n - 2) \\\rm (1980 \degree)/(180 \degree) = (180 \degree(n - 2))/(180 \degree) \\ \rm 11 = n - 2 \\ \rm n = 11+ 2 \\ \rm n = 13\end{array}\end{gathered} \end{gathered}`

4. 4320°

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm 4320 \degree= 180 \degree * \: (n - 2) \\\rm (4320 \degree)/(180 \degree) = (180 \degree(n - 2))/(180 \degree) \\ \rm 24 = n - 2 \\ \rm n = 24 + 2 \\ \rm n = 26\end{array}\end{gathered} \end{gathered}`

5. 1440°

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm 1440 \degree= 180 \degree * \: (n - 2) \\\rm (1440 \degree)/(180 \degree) = (180 \degree(n - 2))/(180 \degree) \\ \rm 8 = n - 2 \\ \rm n = 8 + 2 \\ \rm n = 10\end{array}\end{gathered} \end{gathered}`

B. Calculate the sun of all the interior angle of a polygon having:

6. 5 sides

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm S = 180 \degree * \: (5 - 2) \\\rm S = 180 \degree * \: 3 \\\rm S = 540 \degree \end{array}\end{gathered}\end{gathered}`

7. 7 sides

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm S = 180 \degree * \: (7- 2) \\\rm S = 180 \degree * \: 5 \\\rm S = 900 \degree \end{array}\end{gathered} \end{gathered}`

8. 9 sides

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm S = 180 \degree * \: (9 - 2) \\\rm S = 180 \degree * \: 7 \\\rm S = 1260 \degree \end{array}\end{gathered} \end{gathered}`

9. 10 sides

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm S = 180 \degree * \: (10 - 2) \\\rm S = 180 \degree * \: 8\\\rm S = 1440 \degree \end{array}\end{gathered} \end{gathered}`

10. 11 sides

`\begin{gathered}\begin{gathered}\large\begin{array}{l}\rm S = 180 \degree * \: (n - 2) \\ \rm S = 180 \degree * \: (11 - 2) \\\rm S = 180 \degree * \: 9 \\\rm S = 1620 \degree \end{array}\end{gathered} \end{gathered}`

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