High college Math aid » Geometry » plane Geometry » various other Polygons » exactly how to uncover an angle in a polygon

*


*



*


Correct answer:


Explanation:

The equation to calculation the size of an internal angle is

*
, where 
*
is same to the number of sides.

You are watching: Calculate the measure of one angle in a regular nonagon

For ours question,

*
.

*


Explanation:

To discover the angle of any kind of regular polygon you uncover the variety of sides, 

*
. In this example,
*
.

You then subtract 2 indigenous the variety of sides yielding 5.

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

*

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

*

The answer is 

*
 .


A continuous polygon v

*
 sides has exterior angles that measure up
*
 each. How plenty of sides go the polygon have?


Explanation:

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

*
. Together each angle actions
*
, simply divide 360 by 1.5 to get the variety of angles.

*


Explanation:

To discover the edge of any regular polygon you find the number of sides

*
, i m sorry in this instance is
*
.

You climate subtract

*
 from the number of sides yielding
*
.

Take

*
 and main point it by
*
 degrees to yield a total number of degrees in the consistent nonagon.

*

Then to uncover one individual angle we division

*
 by the total number of angles
*
.

*
 

The price is

*
.


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


Explanation:

The sum of the procedures of the exterior angles of any polygon, one every vertex, is 

*
. In a regular polygon, all of these angles space congruent, so division 360 by 17 to acquire the measure of one exterior angle:

*


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


Explanation:

The sum of the actions of the exterior angle of any type of polygon, one per vertex, is 

*
. In a continuous polygon, every one of these angles are congruent, so division 360 through 23 to gain the measure up of one exterior angle:

*


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


Explanation:

The measure up of each interior angle the a continual polygon with 

*
 sides is 
*
. We deserve to substitute 
*
 to achieve the edge measure:

*


Explanation:

The easiest way to prize this is to keep in mind that, since an inner angle and also an exterior angle kind a direct pair - and also thus, a supplementary pair - each exterior edge would have actually measure 

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

*

Solve for 

*
:

*

*

*

*

The polygon has actually 20 sides.

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