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°

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

2. 1620°

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

3. 1980°

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

4. 4320°

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

5. 1440°

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

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

6. 5 sides

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

7. 7 sides

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

8. 9 sides

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

9. 10 sides

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

10. 11 sides

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

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