Respuesta :
Answer: The correct option is (B) octagon.
Step-by-step explanation: Given that an interior angle of a regular polygon has a measure of 135°.
We are to select the type of the polygon from the given options.
We know that, if n represents the number of sides of a regular polygon and α be its exterior angle, then
[tex]n=\dfrac{360^\circ}{\alpha}.[/tex]
Given that,
an interior angle of the regular polygon is 135°.
So, the measure of an exterior angle will be
[tex]\alpha=180^\circ-135^\circ=45^\circ.[/tex]
Therefore, the number of sides of the regular polygon is
[tex]n=\dfrac{360^\circ}{\alpha}=\dfrac{360^\circ}{45^\circ}=8.[/tex]
So, there are 8 sides of the polygon and hence it is an OCTAGON.
Thus, (B) is the correct option.
