Answer
427.8k+ views
Hint:
Firstly, we will assume the number of sides to be $n$. Then, we will substitute the given value in the formula of an interior angle of a polygon. From this we will calculate the number of sides.
Complete step by step solution:
We are given the measure of each interior angle of a polygon to be $160^0$. Now, let’s assume the number of sides of the given polygon to be $n$.
We know that, the formula to calculate the interior angle of a polygon of $n$ sides is given by
$
Angle = \dfrac{{(n - 2){{180}^0}}}{n} \\
\Rightarrow {160^o} = \dfrac{{(n - 2){{180}^0}}}{n} \\
\Rightarrow {160^0}n = 180n - {360^0} \\
\Rightarrow {180^0}n - {160^0}n = {360^0} \\
\Rightarrow {20^0}n = {360^0} \\
\Rightarrow n = \dfrac{{{{360}^0}}}{{{{20}^0}}} \\
\Rightarrow n = 18 \\
$
So, the given polynomial has 18 sides
Therefore, the right option is B.
Note:
There is an alternate approach to attempt this question using exterior angles.
We are given the interior angle to 1600. We know that Exterior angle of a polygon is given by
(1800-Interior Angle).
So, exterior angle turns out to be ${180^0} - {160^0} = {20^0}$
We also know that the sum of all exterior angles of a polygon is 360 degrees. Hence, the total no. of exterior angles in the given problem can be found as following:
$\dfrac{{{{360}^0}}}{{{{20}^0}}} = 18$
SO, there are 18 angles in for the given polygon. And it is also known that every polygon has an equal number of sides and angles.
Hence, we conclude that the given polygon has 18 sides.
The correct option is B.
Firstly, we will assume the number of sides to be $n$. Then, we will substitute the given value in the formula of an interior angle of a polygon. From this we will calculate the number of sides.
Complete step by step solution:
We are given the measure of each interior angle of a polygon to be $160^0$. Now, let’s assume the number of sides of the given polygon to be $n$.
We know that, the formula to calculate the interior angle of a polygon of $n$ sides is given by
$
Angle = \dfrac{{(n - 2){{180}^0}}}{n} \\
\Rightarrow {160^o} = \dfrac{{(n - 2){{180}^0}}}{n} \\
\Rightarrow {160^0}n = 180n - {360^0} \\
\Rightarrow {180^0}n - {160^0}n = {360^0} \\
\Rightarrow {20^0}n = {360^0} \\
\Rightarrow n = \dfrac{{{{360}^0}}}{{{{20}^0}}} \\
\Rightarrow n = 18 \\
$
So, the given polynomial has 18 sides
Therefore, the right option is B.
Note:
There is an alternate approach to attempt this question using exterior angles.
We are given the interior angle to 1600. We know that Exterior angle of a polygon is given by
(1800-Interior Angle).
So, exterior angle turns out to be ${180^0} - {160^0} = {20^0}$
We also know that the sum of all exterior angles of a polygon is 360 degrees. Hence, the total no. of exterior angles in the given problem can be found as following:
$\dfrac{{{{360}^0}}}{{{{20}^0}}} = 18$
SO, there are 18 angles in for the given polygon. And it is also known that every polygon has an equal number of sides and angles.
Hence, we conclude that the given polygon has 18 sides.
The correct option is B.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)