The number of sides of a regular polygon if each angle is 90o is ____.

# The number of sides of a regular polygon if each angle is 90o is ____.

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### Solution:

We have to find the number of sides when each angle of a polygon is
We know that measure of each interior angle of a regular polygon with n sides is given as,
= × ${180}^{o}$
Substitute 90∘ for θ and solve the equation to determine the value of n,
${90}^{o}$ = × ${180}^{o}$
= $\frac{1}{2}$
Cross-multiply and rearrange the above equation,
2(n - 2) = n
2n - 4 = n
n = 4
Hence, the number of sides is 4.

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