Question

Given a regular octagon and a regular nonagon, which one has the greater interior angle?(Type your answer as the name of the polygon)

Answer 1

Nonagon

Step-by-step explanation:

Each of the interior angles of a polygon is calculated using the formula:

`(180^0\mleft(n-2\mright))/(n)`

An Octagon has 8 sides, therefore:

`\begin{gathered} Each\; \text{Interior Angle=}(180^0(8-2))/(\square) \\ =(180*6)/(8) \\ =(1080^0)/(8) \\ =135^0 \end{gathered}`

A Nonagon has 9 sides, therefore:

`\begin{gathered} Each\; I\text{nterior Angle=}(180^0(9-2))/(9) \\ =(180*7)/(9) \\ =(1260^0)/(9) \\ =140^0 \end{gathered}`

Therefore, the nonagon has a greater interior angle.