Find the sum of interior angles of a 25 sided polgon
Answers
Step-by-step explanation:
As we know the two properties of a polygon that are as follows –
>The measure of each pair of exterior and interior angles of a polygon adds up to 180°
.
>The sum of measures of all the exterior angles of any polygon , irrespective of its number of sides is always 360°
.
Sum of the measures of all the exterior angles and all interior angles of a 25-sided polygon is
25×180°=4500°
.
The sum of measures of all the exterior angles of any polygon , irrespective of its number of sides is always 360°
. So, we are going to subtract the measure of all exterior angles from the sum of the measures of all the exterior angles and all interior angles of a 25-sided polygon so that we can get the interior angles only which can be calculated as –
4500°−360°=4140°
Hence, the sum of all the interior angles of a 25-sided polygon is 4140°
Now , to find the measure of each interior angle of a regular 25-sided polygon we will divide the sum of all interior angles of a 25-sided polygon by the number of sides -25 .
The measure of each iterior angle of a regular 25-sided polygon =4140°/25=165.6°
Therefore , the required answer is 165.6∘.