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

*


*



*


Correct answer:


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.

*

The answer is 

*
 .


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
*
.

*
 

The answer is

*
.

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.


Eastern Washington University, Bachelors, Business: Finance. Western Governors University, Masters, mathematics Education.
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