what is the measure of each interior angle of a regular nonagon.
Answers
Answered by
0
Answer:
Sum of all interior angles of any convex
N
-sided polygon equals to
(
N
−
2
)
180
o
The proof of this is simple. Pick an initial point
O
inside a polygon, connect it with all vertices, forming
N
triangles.
Sum of all angles of these triangles is
N
⋅
180
o
.
To get a sum of all interior angles we should subtract a sum of all angles lying around that initial point
O
, that is we have to subtract
360
o
.
The result for a sum of all interior angles for
N
-sided convex polygon is
N
⋅
180
o
−
360
o
=
(
N
−
2
)
⋅
180
o
In
N
-sided regular polygon all
N
angles are equal, so each is equal to
(
N
−
2
N
)
⋅
180
o
Answered by
1
Answer: s=(n-3) 180 s=(9-3) 180 s=(6) 1180 s=1,080
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