Question

An interior angle of a regular polygon has a measure of 135°. What type of polygon is it? hexagon octagon nonagon decagon

Answer 1

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

$n=\dfrac{360^\circ}{\alpha}.$

Given that,

an interior angle of the regular polygon is 135°.

So, the measure of an exterior angle will be

$\alpha=180^\circ-135^\circ=45^\circ.$

Therefore, the number of sides of the regular polygon is

$n=\dfrac{360^\circ}{\alpha}=\dfrac{360^\circ}{45^\circ}=8.$

So, there are 8 sides of the polygon and hence it is an OCTAGON.

Thus, (B) is the correct option.

Answer 2

its a octagon. e2020 approved, you can trust me