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Problem 493

What is the measure of the interior angle of a regular triangle? A regular quadrilateral? A regular 10 -gon? A regular 2000 -gon?

Expert verified

The interior angle measures of the given regular polygons are as follows: Regular triangle (3 sides) - \(60°\); Regular quadrilateral (4 sides) - \(90°\); Regular 10-gon (10 sides) - \(144°\); Regular 2000-gon (2000 sides) - approximately \(179.64°\).

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Chapter 24

Show that the measure of the exterior angle of a regular n-sided polygon is given by the formula \(360 / \mathrm{n}\).

Chapter 24

What relation holds for an angle of a polygon and its exterior angle?

Chapter 24

The interior angles of a polygon are in arithmetic progression; the least angle is \(120^{\circ}\) and the common difference is \(5^{0}\). Find the number of sides of the polygon.

Chapter 24

\(\underline{A X}\) and \(\underline{B X}\) are two adjacent sides of a regular polygon. If the measure of angle \(\mathrm{ABX}\) equals \(1 / 3\) the measure of angle \(\mathrm{AXB}\), how many sides has the regular polygon?

Chapter 24

Find the number of degrees in the measure of each exterior angle of a regular polygon which has 12 sides.

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