Answer
Verified
476.1k+ views
Hint: Considering n be the greatest common divisor(GCD).Then one polygon has 5n sides,while other has 4n sides and we have to calculate the exterior angle of polygon of 5n-sides and 4n-sides and find their differences
“Complete step-by-step answer:”
Let n be the greatest common divisor (GCD) of the numbers under the question.
Then one polygon has 5n sides, while other has 4n sides
It is well known fact that the sum of exterior angles of each polygon is ${360^ \circ }$
So, the exterior angle of the regular 5n-sided polygon is $\dfrac{{{{360}^ \circ }}}{{5n}}$
Similarly, the exterior angle of the regular 4n-sided polygon is $\dfrac{{{{360}^ \circ }}}{{4n}}$
According to question it is given that difference between the corresponding exterior angles is ${9^ \circ }$
$ \Rightarrow \dfrac{{{{360}^ \circ }}}{{4n}} - \dfrac{{{{360}^ \circ }}}{{5n}} = {9^ \circ }$
$ \Rightarrow \dfrac{{5n - 4n}}{{20{n^2}}} = \dfrac{9}{{360}} = \dfrac{1}{{40}}$
$ \Rightarrow 20n = 40$
$ \Rightarrow n = 2$
So, number of sides in one polygon = $5n = 5 \times 2 = 10$
And number of sides in another polygon $ = 4n = 4 \times 2 = 8$
So this is your answer
NOTE: Whenever we face such a problem the key concept is that we have to remember the exterior angle formula for n sided polygon it will help you in finding your desired answer.
“Complete step-by-step answer:”
Let n be the greatest common divisor (GCD) of the numbers under the question.
Then one polygon has 5n sides, while other has 4n sides
It is well known fact that the sum of exterior angles of each polygon is ${360^ \circ }$
So, the exterior angle of the regular 5n-sided polygon is $\dfrac{{{{360}^ \circ }}}{{5n}}$
Similarly, the exterior angle of the regular 4n-sided polygon is $\dfrac{{{{360}^ \circ }}}{{4n}}$
According to question it is given that difference between the corresponding exterior angles is ${9^ \circ }$
$ \Rightarrow \dfrac{{{{360}^ \circ }}}{{4n}} - \dfrac{{{{360}^ \circ }}}{{5n}} = {9^ \circ }$
$ \Rightarrow \dfrac{{5n - 4n}}{{20{n^2}}} = \dfrac{9}{{360}} = \dfrac{1}{{40}}$
$ \Rightarrow 20n = 40$
$ \Rightarrow n = 2$
So, number of sides in one polygon = $5n = 5 \times 2 = 10$
And number of sides in another polygon $ = 4n = 4 \times 2 = 8$
So this is your answer
NOTE: Whenever we face such a problem the key concept is that we have to remember the exterior angle formula for n sided polygon it will help you in finding your desired answer.
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