
Find the magnitude in radians and degrees of the interior angle of a regular heptagon.
Answer
513.6k+ views
Hint: We know that an interior angle of a regular heptagon is located within the boundary of a heptagon. Also the sum of all interior angles of a polygon can be found using the formula \[S=(n-2)\times 180\] degree where ‘n’ is number of sides of the polygon and to calculate each angle of the regular polygon we will get it by dividing the sum by number of sides.
\[\Rightarrow \]Each angle \[=\left( \dfrac{n-2}{n} \right)\times 180\] degree.
Complete step-by-step answer:
We have been asked the magnitude in radians and degrees of the interior angle of a regular heptagon.
Now as we know that a regular heptagon means a polygon with 7 sides and 7 angles and each of the sides and angles are equal to each other.
\[\Rightarrow \]For a regular heptagon ‘n’ = 7
We know that the measure of each interior angle of a regular polygon having ‘n’ sides is given by as follows:
Each angle \[=\left( \dfrac{n-2}{n} \right)\times 180\] degree
So for a regular octagon, each angle \[=\left( \dfrac{7-2}{7} \right)\times 180\]degree
\[=\dfrac{5}{7}\times 180\] degree
\[=\dfrac{900}{7}\] degree
We know that 1 degree \[=\dfrac{\pi }{180}\] radians
\[\Rightarrow \left( \dfrac{900}{7} \right)=\dfrac{\pi }{180}\times \dfrac{900}{7}\] radians
\[=\dfrac{5\pi }{7}\] radians
Therefore, the magnitude of interior angles of a regular heptagon in radians and degrees are radians \[\dfrac{5\pi }{7}\] and \[\dfrac{900}{7}\] degree respectively.
Note: Be careful while conversion of degree into radians and use the formula 1 degree = \[\dfrac{\pi }{180}\] radians and don’t use 1 degree = \[\dfrac{180}{\pi }\]radians in hurry. Also remember that a regular polygon means each side and angle of the polygon are equal to each other. Also, be careful while calculating each angle of the polygon and use the formula of each angle \[=\left( \dfrac{n-2}{n} \right)\times 180\] degree. Don’t miss that the sum \[\left( n-2 \right)\times 180\] is divided by ‘n’ number of sides of the polygon.
\[\Rightarrow \]Each angle \[=\left( \dfrac{n-2}{n} \right)\times 180\] degree.
Complete step-by-step answer:
We have been asked the magnitude in radians and degrees of the interior angle of a regular heptagon.
Now as we know that a regular heptagon means a polygon with 7 sides and 7 angles and each of the sides and angles are equal to each other.
\[\Rightarrow \]For a regular heptagon ‘n’ = 7
We know that the measure of each interior angle of a regular polygon having ‘n’ sides is given by as follows:
Each angle \[=\left( \dfrac{n-2}{n} \right)\times 180\] degree
So for a regular octagon, each angle \[=\left( \dfrac{7-2}{7} \right)\times 180\]degree
\[=\dfrac{5}{7}\times 180\] degree
\[=\dfrac{900}{7}\] degree
We know that 1 degree \[=\dfrac{\pi }{180}\] radians
\[\Rightarrow \left( \dfrac{900}{7} \right)=\dfrac{\pi }{180}\times \dfrac{900}{7}\] radians
\[=\dfrac{5\pi }{7}\] radians
Therefore, the magnitude of interior angles of a regular heptagon in radians and degrees are radians \[\dfrac{5\pi }{7}\] and \[\dfrac{900}{7}\] degree respectively.
Note: Be careful while conversion of degree into radians and use the formula 1 degree = \[\dfrac{\pi }{180}\] radians and don’t use 1 degree = \[\dfrac{180}{\pi }\]radians in hurry. Also remember that a regular polygon means each side and angle of the polygon are equal to each other. Also, be careful while calculating each angle of the polygon and use the formula of each angle \[=\left( \dfrac{n-2}{n} \right)\times 180\] degree. Don’t miss that the sum \[\left( n-2 \right)\times 180\] is divided by ‘n’ number of sides of the polygon.
Recently Updated Pages
Master Class 10 Computer Science: Engaging Questions & Answers for Success

Master Class 10 Maths: Engaging Questions & Answers for Success

Master Class 10 English: Engaging Questions & Answers for Success

Master Class 10 General Knowledge: Engaging Questions & Answers for Success

Master Class 10 Science: Engaging Questions & Answers for Success

Master Class 10 Social Science: Engaging Questions & Answers for Success

Trending doubts
A number is chosen from 1 to 20 Find the probabili-class-10-maths-CBSE

A boat goes 24 km upstream and 28 km downstream in class 10 maths CBSE

Difference between mass and weight class 10 physics CBSE

Where is the endless fountain of immortal drink pouring class 10 english CBSE

Who gives recognition to political parties as National class 10 social science CBSE

Identify the feminine form of the noun Monk a Monkess class 10 english CBSE
