Answer

Verified

454.2k+ views

Hint- Recall the formula for each interior angle of polygon with respect to the right angles present in it.

Since we have to tell about the number of sides of the second regular polygon hence let the number of sides of second polygon ${\text{ = n}}$

Now it is being given that the number of sides in the first polygon is twice the sides in the first polygon.

So the number of sides of the second polygon ${\text{ = 2n}}$

Now any n sided polygon can be divided into ${\text{(n - 2)}}$triangles. Now the sum of angles of a triangle is 180, therefore the sum of interior angles of a polygon having n sides is ${\text{(2n - 4)}}$right angles. Thus each interior angle of the polygon is $\left( {\dfrac{{2n - 4}}{n}} \right)$right angles.

Hence each interior of first polygon ${\text{ = }}\left( {\dfrac{{4n - 4}}{{2n}}} \right)$right angles

Interior angle of the second polygon $\left( {\dfrac{{2n - 4}}{n}} \right)$right angles

Now it’s given in problem that the angles are in the ratio 3: 4 so we can say that

$\left( {\dfrac{{4n - 4}}{{2n}}} \right):{\text{ }}\left( {\dfrac{{2n - 4}}{n}} \right) = 3:2$

Or

$\dfrac{{\left( {\dfrac{{4n - 4}}{{2n}}} \right)}}{{\left( {\dfrac{{2n - 4}}{n}} \right)}} = \dfrac{3}{2}$

On solving we get

${\text{2}}\left( {\left( {\dfrac{{4n - 4}}{2}} \right)} \right) = 3\left( {2n - 4} \right)$

That is ${\text{4n - 4 = 6n - 12}}$

On solving we get ${\text{n = 4}}$

Thus the number of sides in the first polygon is 8 and the second polygon is 4.

Note- Every time we encounter such problems the key concept involved is that the sum of interior angles of a polygon having n sides is ${\text{(2n - 4)}}$right angles. Thus each interior angle of the polygon is $\dfrac{{2n - 4}}{n}$angles.

Since we have to tell about the number of sides of the second regular polygon hence let the number of sides of second polygon ${\text{ = n}}$

Now it is being given that the number of sides in the first polygon is twice the sides in the first polygon.

So the number of sides of the second polygon ${\text{ = 2n}}$

Now any n sided polygon can be divided into ${\text{(n - 2)}}$triangles. Now the sum of angles of a triangle is 180, therefore the sum of interior angles of a polygon having n sides is ${\text{(2n - 4)}}$right angles. Thus each interior angle of the polygon is $\left( {\dfrac{{2n - 4}}{n}} \right)$right angles.

Hence each interior of first polygon ${\text{ = }}\left( {\dfrac{{4n - 4}}{{2n}}} \right)$right angles

Interior angle of the second polygon $\left( {\dfrac{{2n - 4}}{n}} \right)$right angles

Now it’s given in problem that the angles are in the ratio 3: 4 so we can say that

$\left( {\dfrac{{4n - 4}}{{2n}}} \right):{\text{ }}\left( {\dfrac{{2n - 4}}{n}} \right) = 3:2$

Or

$\dfrac{{\left( {\dfrac{{4n - 4}}{{2n}}} \right)}}{{\left( {\dfrac{{2n - 4}}{n}} \right)}} = \dfrac{3}{2}$

On solving we get

${\text{2}}\left( {\left( {\dfrac{{4n - 4}}{2}} \right)} \right) = 3\left( {2n - 4} \right)$

That is ${\text{4n - 4 = 6n - 12}}$

On solving we get ${\text{n = 4}}$

Thus the number of sides in the first polygon is 8 and the second polygon is 4.

Note- Every time we encounter such problems the key concept involved is that the sum of interior angles of a polygon having n sides is ${\text{(2n - 4)}}$right angles. Thus each interior angle of the polygon is $\dfrac{{2n - 4}}{n}$angles.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE