High institution Math assist » Geometry » aircraft Geometry » various other Polygons » exactly how to discover an angle in a polygon

Explanation:

The equation to calculate the magnitude of an interior angle is

, where
is equal to the number of sides.

You are watching: The figure shows a regular 9 sided polygon

For ours question,

.

Explanation:

To find the edge of any regular polygon you discover the variety of sides,

. In this example,
.

You then subtract 2 native the number of sides yielding 5.

Take 5 and also multiply that by 180 levels to yield the total number of degrees in the continual heptagon.

Then to discover one individual edge we division 900 through the total number of angles, 7.

.

A regular polygon with

sides has exterior angle that measure up
each. How plenty of sides walk the polygon have?

Explanation:

The amount of the exterior angle of any type of polygon, one every vertex, is

. Together each angle procedures
, just divide 360 by 1.5 to obtain the variety of angles.

Explanation:

To uncover the edge of any regular polygon you uncover the variety of sides

, which in this instance is
.

You then subtract

from the variety of sides yielding
.

Take

and multiply it through
degrees to productivity a total number of degrees in the consistent nonagon.

Then to find one individual angle we divide

by the total variety of angles
.

.

See more: The Term &Quot;20 Past 4&Quot; Is Sometimes Used By, The Definition & Meaning

What is the measure of one exterior angle of a continual seventeen-sided polygon (nearest tenth of a degree)?

Explanation:

The amount of the actions of the exterior angles of any kind of polygon, one per vertex, is

. In a continuous polygon, every one of these angles are congruent, so divide 360 by 17 to acquire the measure up of one exterior angle:

What is the measure of one exterior angle of a continual twenty-three-sided polygon (nearest tenth that a degree)?

Explanation:

The amount of the steps of the exterior angles of any kind of polygon, one every vertex, is

. In a continual polygon, every one of these angles are congruent, so division 360 by 23 to obtain the measure up of one exterior angle:

What is the measure of one inner angle that a consistent twenty-three-sided polygon (nearest tenth of a degree)?

Explanation:

The measure up of each internal angle that a continuous polygon with

sides is
. We have the right to substitute
to achieve the edge measure:

Explanation:

The easiest method to prize this is to note that, since an internal angle and an exterior angle type a linear pair - and also thus, a supplementary pair - each exterior edge would have actually measure

. Since 360 split by the variety of sides of a consistent polygon is equal to the measure of one of its exterior angles, we room seeking
such that

Solve for

:

The polygon has 20 sides.

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