Answer:
The measure of one angle of a regular convex 20-gon is 162°
Step-by-step 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
[tex]m=\frac{(n-2)180}{n}[/tex], 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 [tex]m=\frac{(n-2)180}{n}[/tex]
∴ [tex]m=\frac{(20-2)180}{20}[/tex]
∴ [tex]m=\frac{(18)180}{20}[/tex]
∴ [tex]m=\frac{3240}{20}[/tex]
∴ m = 162
∴ The measure of one angle of a regular convex 20-gon is 162°
