Question

find the number of a side of a polygon if the sum of the interior angle is 1800​

Answer 1

Answer:

The polygon has 12 sides.

Step-by-step explanation:

Given :

Sum of interior angles = 1800°

To find :

The number of sides of the polygon

Solution :

Let the number of sides be y

$\textsf{Sum of interior angles = \purple{180(n-2)}}$

$\sf{\implies} \:1800 = 180(y - 2) \\ \\ \sf{\implies} \:1800 = 180y - 360 \\ \\ \sf{\implies} \:180y = 1800 + 360 \\ \\ \sf{\implies} \:180y = 2160 \\ \\ \sf{\implies} \:y = \dfrac{2160}{180} \\ \\ \sf{\implies} \:y = 12$

Number of sides = 12

$\therefore$ The polygon has 12 sides.

Answer 2

${\large\bf{\mid{\overline{\underline{Given:-}}}\mid}}$

• Sum of all interior angles of a polygon = 1800

$\Large\underline\mathfrak{Question}$

• $\textbf{Find the number of sides of Polygon}$ ?

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$

$\textbf{Sum of all interior angles of a polygon with n sides} \\ \\ \red\leadsto \: \red{\huge\boxed{\bf(n - 2) \times 180}} \:$

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$\bold{\boxed{\large{\boxed{\orange{\small{\boxed{\large{\red{\bold{\:Answer}}}}}}}}}} \:$

$\green{\texttt{Putting value in above Formula we get}}$

$\red\longrightarrow \sf (n - 2) \times 180 = 1800 \\ \\ \red\longrightarrow \sf \: (n - 2) = \frac{1800}{180} \\ \\ \red\longrightarrow \sf \: n - 2 = 10 \\ \\ \red\longrightarrow \bf \: \large\red{\boxed{\tt\blue{n}\purple{=} \green {12} \orange,\pink{sides}}}</p><p>$

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Hence, Number of sides of Polygon will be 12 ...

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$\large\bf\ \red\bigstar\underline\texttt{Extra\:Brainly\:Knowledge:-}\red\bigstar \:$

→ Each interior angle of Polygon = (n-2)*180/n

→ Each exterior angle of Polygon = 360°/n .

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