Find the measure of the exterior angles of the following regular polygons: a triangle, a quadrilateral, a pentagon, an octagon, a decagon, a 30-gon, a 50-gon, and a 100-gon.

The exterior angle of the polygons of a triangle, a quadrilateral, a pentagon, an octagon, a decagon, a 30-gon, a 50-gon, and a 100-gon all are regular polygons are 120, 90, 72, 45, 36, 12, 7.2, and 3.6 respectively.

What is the angle?

Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Given

A triangle, a quadrilateral, a pentagon, an octagon, a decagon, a 30-gon, a 50-gon, and a 100-gon all are regular polygons.

To find

The exterior angle of the polygons.

How do find the exterior angle of the polygons?

We know the formula of the exterior angle.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}[/tex]

For a triangle number of sides is 3.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{3 }\\\\\rm Exterior\ angle = 120^o[/tex]

For a quadrilateral number of sides is 4.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{4 }\\\\\rm Exterior\ angle = 90^o[/tex]

For a pentagon number of sides is 5.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{5 }\\\\\rm Exterior\ angle = 72^o[/tex]

For an octagon number of sides is 8.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{8 }\\\\\rm Exterior\ angle = 45^o[/tex]

For a decagon number of sides is 10.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{10 }\\\\\rm Exterior\ angle = 36^o[/tex]

For a 30-gon number of sides is 30.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{30}\\\\\rm Exterior\ angle = 12^o[/tex]

For a 50-gon number of sides is 50.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{50 }\\\\\rm Exterior\ angle = 7.2^o[/tex]

For a 100-gon number of sides is 100.

[tex]\rm Exterior\ angle = \dfrac{360^o}{Number\ of\ sides}\\\\\rm Exterior\ angle = \dfrac{360^o}{100 }\\\\\rm Exterior\ angle = 3.6^o[/tex]

Thus, the exterior angle of the polygons of a triangle, a quadrilateral, a pentagon, an octagon, a decagon, a 30-gon, a 50-gon, and a 100-gon all are regular polygons are 120, 90, 72, 45, 36, 12, 7.2, and 3.6 respectively.

More about the angles link is given below.

https://brainly.com/question/15767203