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3 years ago

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

Mathematics

2 answers:

yan [13]3 years ago

8 0

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.

Juli2301 [7.4K]3 years ago

7 0

its a octagon. e2020 approved, you can trust me

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