Question

in a regular polygon the measure of each exterior angle is 25% of the measure of each interior angle calculate the number of sides of the polygon

Answer 1

Dear student,
suppose the number of sides of the polynomial is 'n' and a measure of each interior angle is 'x'
According to the question,
Each interior angle is calculated by using the expression as follows
x= (n-2)*180/n
Each exterior angle is calculated by using the expression as follows
Each exterior angle = 360/n
Each exterior angle is equal to the 25% of interior angle,
Thus, each exterior angle= 25%*x
Each exterior angle=x/4
substitute the value of x in the above expression
Each exterior angle = ((n-2)*180/n)*1/4
substitute 360/n for each exterior angle
360/n=((n-2)*180/n)*1/4
360*4=180*n - 360
360*5=180*n
n=10
Therefore, a number of sides of the polygon(n) is 10.
regards