Answer:
see the explanation
Step-by-step explanation:
we know that
The sum of the interior angles in any polygon is given by the formula
[tex]S=(n-2)180^o[/tex]
where
n is the number of sides
so
To find out the sum of the interior angles in given shape, substitute in the formula the number of sides of the figure (n) to obtain S
Examples
1) The figure is a quadrilateral
A quadrilateral has four sides
so
[tex]n=4[/tex]
substitute in the formula
[tex]S=(4-2)180^o=360^o[/tex]
therefore
The sum of the interior angles in a quadrilateral is 360 degrees
2) The figure is a triangle
A triangle has three sides
so
[tex]n=3[/tex]
substitute in the formula
[tex]S=(3-2)180^o=180^o[/tex]
therefore
The sum of the interior angles in a triangle is 180 degrees
