Question

Знайдіть міру внутрішнього і центрального кутів правильного 9 -кутника​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Finding the Measure of Interior and Central Angles of a Regular 9-gon

To find the measure of the interior and central angles of a regular 9-gon, we can use the formula:

Interior Angle = (n-2) * 180 / n

where n is the number of sides of the polygon.

For a regular 9-gon, n = 9. Plugging this value into the formula, we get:

Interior Angle = (9-2) * 180 / 9

Simplifying the equation:

Interior Angle = 7 * 180 / 9

Calculating the value:

Interior Angle = 140 degrees

Therefore, the measure of each interior angle of a regular 9-gon is 140 degrees.

Now, let's find the measure of the central angle of a regular 9-gon. The central angle is formed by two radii of the polygon and measures the angle at the center of the polygon.

To find the measure of the central angle, we can use the formula:

Central Angle = 360 / n

where n is the number of sides of the polygon.

For a regular 9-gon, n = 9. Plugging this value into the formula, we get:

Central Angle = 360 / 9

Simplifying the equation:

Central Angle = 40 degrees

Therefore, the measure of each central angle of a regular 9-gon is 40 degrees.

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