Respuesta :
The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
To solve the given problem, it is necessary to know about the polygon. A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.
- A regular polygon refers to a multi-sided convex figure where all the sides are equal in length and all the angles have equal degree measures.
For example: -
- The triangle is a polygon that has 3 interior angles.
- The square is a polygon that has 4 interior angles.
- The pentagon is a polygon that has 5 interior angles.
The formula for the interior angle of a regular polygon is given by,
[tex]= \dfrac{ (n-2) \times 180}{n}[/tex]
Here, n is the number of sides.
Then the calculation is given as,
For triangle ( n = 3 sides ),
[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (3-2) \times 180}{3}\\\\=60 \;\rm degrees[/tex]
For square ( n = 4 sides ),
[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (4-2) \times 180}{4}\\\\=90 \;\rm degrees[/tex]
For pentagon ( n = 5 sides ),
[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (5-2) \times 180}{5}\\\\=108 \;\rm degrees[/tex]
Thus, we can conclude that the interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
Learn more about the interior angles here:
https://brainly.com/question/10638383
The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
We have to determine, The measure of one interior angle in each regular polygon.
A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.
A regular polygon refers to a multi-sided convex figure where all the sides are equal in length and all the angles have equal degree measures.
The formula for the interior angle of a regular polygon is given by,
[tex]= \frac{(n-2)\times180}{n}[/tex]
Where, n is number of sides.
The triangle is a polygon that has 3 interior angles.
The square is a polygon that has 4 interior angles.
The pentagon is a polygon that has 5 interior angles.
For triangle ( n = 3 sides ),
[tex]= \frac{(3-2)\times 180}{3} \\\\= \frac{180}{3} \\\\= 60degree[/tex]
For square ( n = 4 sides ),
[tex]= \frac{(4-2)\times 180}{4} \\\\= \frac{360}{4} \\\\= 90degree[/tex]
For pentagon ( n = 5 sides ),
[tex]= \frac{(5-2)\times 180}{5} \\\\= \frac{540}{5} \\\\= 108degree[/tex]
Hence, The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
For more information about Regular Polygon click the link given below.
https://brainly.com/question/17058969?
