Answer
Verified
375.3k+ views
Hint: We first describe how the interior and exterior angles of a n-sided regular polygon works. We find their general values. Then using the given values of exterior angle and the formula of exterior angles $\dfrac{2\pi }{n}$, we find the number of sides. If the value is integer, then polygon exists and if value is fraction, then the polygon doesn’t exist.
Complete step-by-step solution:
We know that for a n-sided regular polygon, the exterior angles would be all equal and the value will be $\dfrac{2\pi }{n}$.
Now from the given values of interior angles we found the exterior angles as the sum of interior and exterior angles is $\pi $. We use that value to find if the value of n is integer or fraction. If it’s integer then the polygon exists and if it’s a fraction then the polygon doesn’t exist.
For the exterior angle ${{40}^{\circ }}$, we assume the polygon is p-sided then the value of the exterior angles will be $\dfrac{2\pi }{p}$.
So, $\dfrac{2\pi }{p}=40$. We solve it to get the value of p as \[p=\dfrac{360}{40}=9\].
The regular polygon exists and has 9 sides.
Note: We also can use the formula of interior angles to find the values. We know that for a n-sided regular polygon, the interior angles would all be equal and the value will be $\dfrac{\pi }{n}\left( n-2 \right)$. We put the values of the given interior angles $180-40-140$ and try to find the value of n.
Complete step-by-step solution:
We know that for a n-sided regular polygon, the exterior angles would be all equal and the value will be $\dfrac{2\pi }{n}$.
Now from the given values of interior angles we found the exterior angles as the sum of interior and exterior angles is $\pi $. We use that value to find if the value of n is integer or fraction. If it’s integer then the polygon exists and if it’s a fraction then the polygon doesn’t exist.
For the exterior angle ${{40}^{\circ }}$, we assume the polygon is p-sided then the value of the exterior angles will be $\dfrac{2\pi }{p}$.
So, $\dfrac{2\pi }{p}=40$. We solve it to get the value of p as \[p=\dfrac{360}{40}=9\].
The regular polygon exists and has 9 sides.
Note: We also can use the formula of interior angles to find the values. We know that for a n-sided regular polygon, the interior angles would all be equal and the value will be $\dfrac{\pi }{n}\left( n-2 \right)$. We put the values of the given interior angles $180-40-140$ and try to find the value of n.
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
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE