Question

What is the measure of each interior angle of a stop sign?

Answer 1

Hint: The shape of a stop sign is of a regular octagon. So, we need to find the measure of each interior angle of the octagon. Now, an octagon has 8 sides and 8 angles and all these angles and sides are equal.

Formula used:
The formula used to find the interior angle of octagon is
Interior angle$ = 180 - $Exterior angle
Exterior angle $ = \dfrac{{360}}{n}$

Complete step by step solution:
In this question, we are supposed to find the measure of each interior angle of a stop sign.
First of all, what is the shape of the stop sign?
The stop sign has the following shape.

Here, we can see that the shape of the stop sign is a regular octagon.
Octagon has eight sides and eight angles.
All these sides and angles are equal to each other.
So, to find the measure of interior angles of a stop sign, we need to find the interior angles of a regular octagon.
Now, the formula to find the interior angle of an octagon is given by
$ \Rightarrow $Interior angle$ = 180 - $exterior angle
And as an octagon has 8 sides that means $n=8$, the formula for exterior angle is given by
$ \Rightarrow $Exterior angle $ = \dfrac{{360}}{n} = \dfrac{{360}}{8} = 45$
Hence, Interior angle $ = 180 - 45 = 135$.
Therefore, the measure of each interior angle in a stop sign is $135$.

Note:
The difference between regular octagon and irregular octagon is that regular octagon has all the sides and angles equal and an irregular octagon has irregular sides and angles that means different sides and different angles.