Question

A. Regular octagon
no.of sides =8
(n-2)×180=

B. Regular nonagon
no.of sides =9
(n-2)×180=
please answer this 2 question now ​

Answer 1

Step-by-step explanation:

quadrilaterals, pentagons, hexagons and so on.

Regular

A "Regular Polygon" has:

all sides equal and

all angles equal.

Otherwise it is irregular.

pentagon regular irregular pentagon

Regular Pentagon Irregular Pentagon

Here we look at Regular Polygons only.

Properties

So what can we know about regular polygons? First of all, we can work out angles.

exterior angle

Exterior Angle

The Exterior Angle is the angle between any side of a shape,

and a line extended from the next side.

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All the Exterior Angles of a polygon add up to 360°, so:

Each exterior angle must be 360°/n

(where n is the number of sides)

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external angle of regular octagon

Exterior Angle

(of a regular octagon)

Example: What is the exterior angle of a regular octagon?

An octagon has 8 sides, so:

Exterior angle = 360° / n

= 360° / 8

= 45°

exterior interior angle

Interior Angles

The Interior Angle and Exterior Angle are measured from the same line, so they add up to 180°.

Interior Angle = 180° − Exterior Angle

We know the Exterior angle = 360°/n, so:

Interior Angle = 180° − 360°/n

Which can be rearranged like this:

Interior Angle = 180° − 360°/n

= (n × 180° / n) − (2 × 180° / n)

= (n−2) × 180°/n

So we also have this:

Interior Angle = (n−2) × 180° / n

Example: What is the interior angle of a regular octagon?

A regular octagon has 8 sides, so:

Exterior Angle = 360° / 8 = 45°

Interior Angle = 180° − 45° = 135°

internal angle of regular octagon

Interior Angle

(of a regular octagon)

Or we could use:

Interior Angle = (n−2) × 180° / n

= (8−2) × 180° / 8

= 6 × 180° / 8

= 135°

Example: What are the interior and exterior angles of a regular hexagon?

regular hexagon

A regular hexagon has 6 sides, so:

Exterior Angle = 360° / 6 = 60°

Interior Angle = 180° − 60° = 120°