Question

Найдите внутренний и внешний углы правильного девятиугольника

Answer 1

Для начала найдем радиус внутренего угла
1)уголА=(n-2)180/n
А=140
2)Внешний угол=180-140=40

Answer 2

Finding the Internal and External Angles of a Regular Nonagon

A regular nonagon is a nine-sided polygon where all the sides and angles are equal. Let's find the internal and external angles of a regular nonagon.

Internal Angles: The formula to find the measure of each internal angle in a regular nonagon is given by: \[ \text{Internal angle} = \frac{180^\circ \times (n-2)}{n} \] Where \( n \) is the number of sides, which in this case is 9.

Using the formula: \[ \text{Internal angle} = \frac{180^\circ \times (9-2)}{9} = \frac{180^\circ \times 7}{9} = 140^\circ \]

External Angles: The formula to find the measure of each external angle in a regular nonagon is given by: \[ \text{External angle} = \frac{360^\circ}{n} \] Where \( n \) is the number of sides, which in this case is 9.

Using the formula: \[ \text{External angle} = \frac{360^\circ}{9} = 40^\circ \]

So, the internal angle of a regular nonagon is 140 degrees and the external angle is 40 degrees.