Answer
Verified
417.6k+ views
Hint:First of all, find the sum of interior angles of the hexagon and so that we can find each interior angle. Find the angle of each exterior angle of the hexagon to find the sum of the exterior angles of the hexagon.
Complete step-by-step answer:
Number of sides in a hexagon \[n = 6\] as shown in the below figure:
We know that sum of interior angles of a polygon \[ = \left( {n - 2} \right)\pi \]
So, sum of interior angles of the hexagon \[ = \left( {6 - 2} \right)\pi = 4\pi \]
If the sum of 6 interior angles is \[4\pi \], then one angle is equal to \[\dfrac{{4\pi }}{6} = {120^0}\]
We know that the sum of interior and exterior angle is equal to \[{180^0}\] i.e.,
Interior angle + Exterior angle = \[{180^0}\]
Exterior angle = \[{180^0} - \] Interior angle
= \[{180^0} - {120^0} = {60^0}\]
As there are 6 exterior angles in a hexagon, the sum of the exterior angles in hexagon is \[6 \times {60^0} = {360^0}\]
Hence the sum of the exterior angles in the hexagon is \[{360^0}\]
Thus, the correct option is A. \[{360^0}\]
Note:Hexagon is one of the polygons. Hexagon has 6 equal sides. The sum of interior and exterior angle is equal to \[{180^0}\]. The sum of interior angles of a polygon is equal to \[\left( {n - 2} \right)\pi \] where \[n\] is the number of sides of the polygon.
Complete step-by-step answer:
Number of sides in a hexagon \[n = 6\] as shown in the below figure:
We know that sum of interior angles of a polygon \[ = \left( {n - 2} \right)\pi \]
So, sum of interior angles of the hexagon \[ = \left( {6 - 2} \right)\pi = 4\pi \]
If the sum of 6 interior angles is \[4\pi \], then one angle is equal to \[\dfrac{{4\pi }}{6} = {120^0}\]
We know that the sum of interior and exterior angle is equal to \[{180^0}\] i.e.,
Interior angle + Exterior angle = \[{180^0}\]
Exterior angle = \[{180^0} - \] Interior angle
= \[{180^0} - {120^0} = {60^0}\]
As there are 6 exterior angles in a hexagon, the sum of the exterior angles in hexagon is \[6 \times {60^0} = {360^0}\]
Hence the sum of the exterior angles in the hexagon is \[{360^0}\]
Thus, the correct option is A. \[{360^0}\]
Note:Hexagon is one of the polygons. Hexagon has 6 equal sides. The sum of interior and exterior angle is equal to \[{180^0}\]. The sum of interior angles of a polygon is equal to \[\left( {n - 2} \right)\pi \] where \[n\] is the number of sides of the polygon.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Select the word that is correctly spelled a Twelveth class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE