Question

How many right angles does a hexagon have?

Answer 1

Hint:In the given question, we have been given the name of a geometric shape, a polygon. Then, we have been asked how many angles of a particular kind are there in the polygon. To answer that, we first need to know how the given polygon looks like, what is the total sum of the angles.

Formula Used:
The total sum of the angles in a polygon with \[n\] sides is,
\[ = 180\left( {n - 2} \right)\]

Complete step by step answer:

The total sum of angles in a hexagon, a polynomial with \[6\] sides, is
\[180 \times \left( {6 - 2} \right) = 720^\circ \]
In a regular hexagon, all the angles are equal, because of which the measure of each angle is \[120^\circ \], making the regular hexagon have no possible right angles. Hence, only an irregular hexagon can have right angles.
Now, we know that the number of angles in a hexagon is \[6\]. Hence, the maximum number of right angles in a hexagon is going to be the integer just smaller than \[6\], which is:
\[6 - 1 = 5\]

Hence, a hexagon can have \[5\] right angles.

Note: Sometimes, for solving the question, we have to go beyond the obvious. We have to think about the consequences of the answer that we give. In a regular hexagon, all the angles are equal, because of which the measure of each angle is \[120^\circ \], making the regular hexagon have no possible right angles. Hence, only an irregular hexagon can have right angles. Then, by using this fact, we found the maximum possible number of right angles in a hexagon.