Question

How many obtuse angles does a hexagon have?

Answer 1

Hint: The above question is based on the concept of finding angles of a polygon. The main approach towards solving the above question with the help of sum of interior angles and the number of sides of the polygon will decide the number of angles the hexagon has.

Complete step by step solution:
Hexagon is also called a polygon. A polygon can be any 2-dimensional shape which is formed with straight lines with a finite number of sides. Hexagon is just an example for polygon. In geometry, hexagon can be defined as a shape which has six sides.
The above given figure shows that all the sides of the hexagon are equal. And all the angles are equal to 120. There are two types of angles that is interior or exterior angles.
Since the sum of interior angles is \[\left( {n - 2} \right) \times 180\] where n is the number of sides.
Here the number of sides is 6, therefore by substituting 6 we get 720.Since there are six sides, six vertices we get six interior angles.
So, dividing 720 by 6 we get 120.So each angle is 120 inside.
The exterior angle is the angle between any side of a shape and line extended from the next side.The exterior angle is 60 from every side.
Obtuse angle means the angle between 90 and 180.
So here all the six interior angles are obtuse since its angle is 120.

Note: An important thing to note is that the sum of interior and exterior angle is 180.Since the interior angle is 120 ,therefore \[180 - 120\] will give 60.Since 60 is an acute angle therefore there are only six obtuse angles present which are interior angles.