Answer:
Sum of the interior angles = (n-2) x 180°
where
n is the number of sides of the polygon
Step-by-step explanation:
The formula for the sum of the interior angles of a polygon is:
[tex]sum=(n-2)*180[/tex]
where
[tex]sum[/tex] is the sum of the interior angle of the polygon
[tex]n[/tex] is the number of polygons
Let's check the formula using an example:
We want to find the sum of the interior angles of a square, we know that a square has 4 sides, so [tex]n=4[/tex].
Replacing values
[tex]sum=(4-2)*180[/tex]
[tex]sum=(2)*180[/tex]
[tex]sum=360[/tex]
We can apply the same procedure to any convex polygon with n sides.
Answer:
Sum of the interior angles = (n - 2) × 180°.
Where n is the number of sides of the polygon.
Explanation:
The formula (n - 2) × 180° is valid for any convex polygon.
A convex polygon is one whose interior angles (every interior angle) measure less than 180°.
You can prove and remember that formula following this reasoning:
For example, for a pentagon, a polygon with 5 sides, you can can draw 5 - 2 = 3 diagonals from one vertex, and so obtain 3 triangles. Then the sum of the interior angles shall be (n - 2) × 180° = (5 - 2) × 180° = 3 × 180° = 540°.
