Question

How much is each angle of a 25 sided regular polygon? How much is each outer angle?​

Answer 1

Answer:

Sum of the measures of all the exterior angles of any polygon, irrespective of its number of sides is always

360

∘

.

As the measure of each pair of exterior and interior angles of a polygon adds up to

180

∘

,

Sum of the measures of all the exterior angles and all interior angles of a 25-sided polygon is

25

×

180

∘

=

4500

∘

Hence, sum of all the interior angles of of a 25-sided polygon is

(

4500

−

360

)

∘

=

4140

∘

From the above information, we can see that for an

n

sided polygon

Sum of interior angles =

(

n

−

2

)

⋅

180

∘