Question

How many acute angles does a hexagon have?

Answer 1

Hint: From the given question we are asked to find the number of acute angles are there for a hexagon figure. For solving this question we will take the help of the definition of a hexagon. We check the total angle for an hexagon using the diagram or figure of a hexagon and we will then see what kind of angles it can have , whether acute angle or obtuse angle etc.. so, we proceed with our solution.

Complete step by step solution:
Generally a regular hexagon is a closed shape polygon which has six sides where all the sides are equal.
In the case of a regular polygon all sides along with all the angles are equal.
So, for our regular hexagon we have all sides and angles are equal.
The figure for a regular hexagon will be as follows.

Here we can see it has \[6\] sides and the total angle count for a \[6\] sided polygon is \[{{720}^{\circ }}\].
Because, we know that, and that a hexagon has \[6\] angles. We can simply divide,
\[\Rightarrow \dfrac{{{720}^{\circ }}}{6}={{120}^{\circ }}\]
Since \[{{120}^{\circ }}\] is a bigger angle than \[{{90}^{\circ }}\], we know that all those angles are obtuse angles and not acute angles.
Therefore, we can say that it has no acute angles in it.

Note: Students should have good knowledge in the concept of polygons. Students should know the number of sides and angles a hexagon consists of. We must note that we have taken a regular hexagon as we are not mentioned as a hexagon in our question so that it makes our solution an accurate one.