In a 12- sided polygon
a) How many diagonals can be drawn from a vertex to the opposite vertices ?
b) How many triangles will be formed ?
c) Find the sum of inner angles of the polygon.
Answers
Given : 12- sided polygon
To Find : a) How many diagonals can be drawn from a vertex to the opposite vertices ?
b) How many triangles will be formed ?
c) Find the sum of inner angles of the polygon
Solution:
Diagonal formed from one vertex to all other vertices
n-3 diagonals can be formed
= 12 - 3 = 9
Number of Total Diagonals = n(n-3)/2
= 12(12-3)/2
= 12 * 9 /2
= 54
54 Diagonal
triangles formed when drawing line segments from one vertex of a polygon to all the others.
= n - 3
= 12 - 3
= 9
sum of inner angles of the polygon.
= (n-2)*180
= (12 - 2) * 180
= 1800°
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