to find the number of sides in a polygon.

Asked by  | 16th Feb, 2014, 09:39: AM

Expert Answer:

Sum of the interior angles of a convex polygon S = 180(n - 2), where n is the number of sides of a polygon.
 
We need to find the value of n such that, there are 5 right angles and each of the remaining angles are equal to 195.
 
Therefore, the number of sides should be greater than 5.
 
Thus, S equals 5 cross times 90 degree plus open parentheses n minus 5 close parentheses cross times 195 degree
Equating the values of S, we have,
 
180 degree open parentheses n minus 2 close parentheses equals 5 cross times 90 degree plus open parentheses n minus 5 close parentheses cross times 195 degree rightwards double arrow 180 degree n minus 360 degree equals 450 degree plus 195 n minus 975 degree rightwards double arrow 525 degree minus 360 degree equals 195 n minus 180 n rightwards double arrow 15 n equals 165 degree rightwards double arrow n equals 165 over 15 equals 11
Thus, the number of sides in the polygon is 11.

Answered by  | 16th Feb, 2014, 11:13: AM

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