Answer
Verified
390.3k+ views
Hint: We are given a regular polygon whose exterior angle is 15 degrees and we have to find the sides of the polygon. We know that the sum of the exterior angles of a polygon is \[{{360}^{\circ }}\]. So, if we divide the total sum of the exterior angle of a polygon by the exterior angle, then, we will get the value of the number of sides of the polygon.
Complete step by step solution:
According to the question given to us, we are given the value of an exterior angle of a polygon. The value is 15 degrees. And using that, we have to find the number of sides of that polygon.
Polygon refers to the geometrical shape made using a finite number of straight lines and which are closed.
Example – Square, Triangle
We know that the total sum of exterior angles of any polygon is \[{{360}^{\circ }}\].
And if we want to know the exterior angle of any polygon, we divide \[{{360}^{\circ }}\] by the number of sides, ‘n’ of that particular polygon.
That is, \[\dfrac{{{360}^{\circ }}}{n}\].
For example – Square has 4 sides, so the value of exterior angle is \[\dfrac{{{360}^{\circ }}}{4}={{90}^{\circ }}\]
So, if we want to find the number of sides then, we will divide \[{{360}^{\circ }}\] by the exterior angle.
We have,
\[\dfrac{{{360}^{\circ }}}{n}={{15}^{\circ }}\]
Rearranging the above equation in terms of ‘n’, we have,
\[\Rightarrow \dfrac{{{360}^{\circ }}}{{{15}^{\circ }}}=n\]
\[\Rightarrow n=\dfrac{{{360}^{\circ }}}{{{15}^{\circ }}}\]
Solving the above expression, we get the value as,
\[\Rightarrow n=24\]
Therefore, the number of sides of the polygon is 24 sides.
Note: The formula used for finding the number of sides should not be confused and should be used appropriately. The calculations should be done correctly and step-wise. And also, the exterior angle should not be confused with the interior angle, both are different in every aspect.
Sum of exterior angles of any polygon is \[{{360}^{\circ }}\], but the sum of interior angles is different for different polygon and can be calculated by using the formula \[(n-2)\times {{180}^{\circ }}\], where \[n\] is the number of sides of that polygon.
Complete step by step solution:
According to the question given to us, we are given the value of an exterior angle of a polygon. The value is 15 degrees. And using that, we have to find the number of sides of that polygon.
Polygon refers to the geometrical shape made using a finite number of straight lines and which are closed.
Example – Square, Triangle
We know that the total sum of exterior angles of any polygon is \[{{360}^{\circ }}\].
And if we want to know the exterior angle of any polygon, we divide \[{{360}^{\circ }}\] by the number of sides, ‘n’ of that particular polygon.
That is, \[\dfrac{{{360}^{\circ }}}{n}\].
For example – Square has 4 sides, so the value of exterior angle is \[\dfrac{{{360}^{\circ }}}{4}={{90}^{\circ }}\]
So, if we want to find the number of sides then, we will divide \[{{360}^{\circ }}\] by the exterior angle.
We have,
\[\dfrac{{{360}^{\circ }}}{n}={{15}^{\circ }}\]
Rearranging the above equation in terms of ‘n’, we have,
\[\Rightarrow \dfrac{{{360}^{\circ }}}{{{15}^{\circ }}}=n\]
\[\Rightarrow n=\dfrac{{{360}^{\circ }}}{{{15}^{\circ }}}\]
Solving the above expression, we get the value as,
\[\Rightarrow n=24\]
Therefore, the number of sides of the polygon is 24 sides.
Note: The formula used for finding the number of sides should not be confused and should be used appropriately. The calculations should be done correctly and step-wise. And also, the exterior angle should not be confused with the interior angle, both are different in every aspect.
Sum of exterior angles of any polygon is \[{{360}^{\circ }}\], but the sum of interior angles is different for different polygon and can be calculated by using the formula \[(n-2)\times {{180}^{\circ }}\], where \[n\] is the number of sides of that polygon.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
A group of fish is known as class 7 english CBSE
The highest dam in India is A Bhakra dam B Tehri dam class 10 social science CBSE
Write all prime numbers between 80 and 100 class 8 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Onam is the main festival of which state A Karnataka class 7 social science CBSE
Who administers the oath of office to the President class 10 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Kolkata port is situated on the banks of river A Ganga class 9 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE