The number of sides of a regular polygon if each angle is 90o is ____. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

We have to find the number of sides when each angle of a polygon is

90^{o}

We know that measure of each interior angle of a regular polygon with n sides is given as,

θ

\frac{n - 2}{n}

180^{o}

Substitute 90∘ for θ and solve the equation to determine the value of n,

90^{o}

\frac{n - 2}{n}

180^{o}

\frac{n - 2}{n}

\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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