The inside corner of a regular polygon is 4 times the outside corner. Find the perimeter of this polygon if its side is 21 cm.

univerkov | August 19, 2021 | education

Let the angle BОС = X0, then the angle AOB = 4 * X0.

The inner corner AOB and the outer corner BOC are adjacent angles, then X + 4 * X = 180.

5 * X = 180.

X = BOC = 180/5 = 360.

AOB = 4 * 36 = 144.

Then 144 = (n – 2) * 180 / n.

144 * n = 180 * n – 360.

n = 360/36 = 10.

The polygon has 10 faces. Then P = 10 * 21 = 210 cm.

Answer: The perimeter is 210 cm.

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