Question

the measure of each interior angle of a regular n - gon is 90°. determine the value of n. n =

Explanation:

Step1: Recall the formula for interior angle of regular n - gon

The formula for the measure of each interior angle of a regular \(n\) - gon is \(\frac{(n - 2)\times180^{\circ}}{n}\).

Step2: Set up the equation

We know that each interior angle is \(90^{\circ}\), so we set up the equation \(\frac{(n - 2)\times180^{\circ}}{n}=90^{\circ}\).

Step3: Solve the equation

Multiply both sides of the equation by \(n\): \((n - 2)\times180 = 90n\)
Expand the left - hand side: \(180n-360 = 90n\)
Subtract \(90n\) from both sides: \(180n-90n-360=90n - 90n\)
Simplify: \(90n-360 = 0\)
Add 360 to both sides: \(90n=360\)
Divide both sides by 90: \(n=\frac{360}{90}=4\)

Answer:

\(n = 4\)