Question

What is the measure of one angle of a regular convex 20-gon

Answer 1

The measure of one angle of a regular convex 20-gon is 162°

Explanation:

* Lets explain how to solve the problem

- A convex polygon is a polygon with all the measures of its interior

angles less than 180°

- In any polygon the number of its angles equal the number of its sides

- A regular polygon is a polygon that is all angles are equal in measure

and all sides are equal in length

- The rule of the measure of an angle of a regular polygon is

`m=((n-2)180)/(n)`, where m is the measure of each interior

angle in the polygon and n is the numbers of the sides or the angles

of the polygon

* Lets solve the problem

- The polygon is convex polygon of 20 sides (20 angles)

- The polygon is regular polygon

∵ The number of the sides of the polygon is 20 sides

∴ n = 20

∵ The polygon is regular

∴ All angles are equal in measures

∵ The measure of each angle is
`m=((n-2)180)/(n)`

∴
`m=((20-2)180)/(20)`

∴
`m=((18)180)/(20)`

∴
`m=(3240)/(20)`

∴ m = 162

∴ The measure of one angle of a regular convex 20-gon is 162°