Concept explainers
To show:There is no
Explanation of Solution
Given information
The ratio of no. of diagonals to the sum of the measures of the polygon’s angle is 1 to 18
Formula used
No. of diagonals in a polygon of n − sides is given by:
n (n − 3 ) and
Sum of the measures of the polygon’s angles is given by:
180 (n − 2)
Proof:
Since, given that
The ratio of no. of diagonals to the sum of the measures of the polygon’s angle is :
1 : 18, i.e.
For polygon of n − sides
No. of diagonals: sum of measures of angles in polygon is 1:18
n (n − 3) : 180 (n − 2)::1:18
Since, equation:
has no rational solution,
Thus, no such polygon will exist
Hence proved
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