intermediate Geometry aid » aircraft Geometry » Hexagons » just how to discover an angle in a hexagon

There is a continuous hexagon through a side size of

*
. What is the measure up of an inner angle?


*


*


*


*


Explanation:

Given the the hexagon is a consistent hexagon, this way that all the side length are congruent and also all interior angles space congruent. The concern requires united state to settle for the measure of an internal angle. Given the aforementioned definition of a consistent polygon, this means that there should only be one correct answer.

You are watching: What is the measure of one exterior angle of a regular hexagon?

In order to fix for the answer, the question provides additional information that isn"t necessarily required. The measure of an interior angle can be fixed for making use of the equation:

*
 where
*
 is the variety of sides the the polygon.

In this case,

*
.

For this problem, the information around the side length may be negated.

*

*

*

*


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Example inquiry #2 : just how To find An angle In A Hexagon


What is the inner angle of a consistent hexagon if the area is 15?


Possible Answers:
Correct answer:

*


Explanation:

The area has actually no relevance to find the edge of a constant hexagon.

There room 6 sides in a constant hexagon. Usage the following formula to recognize the inner angle.

*

Substitute 

*
 sides to recognize the amount of all internal angles the the hexagon in degrees.

*

Since there room 6 sides, division this number by 6 to determine the value of each interior angle.

*


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Example question #3 : just how To find An edge In A Hexagon


Given: constant Hexagon 

*
 with center 
*
. Construct segments 
*
 and 
*
 to type Quadrilateral .

True or false: Quadrilateral 

*
 is a rectangle.


Possible Answers:

True


False


Correct answer:

False


Explanation:

Below is regular Hexagon 

*
 with center 
*
, a segment attracted from 
*
 to every vertex - the is, each of its radii drawn.

*

Each edge of a continual hexagon measures 

*
; by symmetry, every radius bisects an angle the the hexagon, so 

*
.

The angle of a rectangle must measure 

*
, so it has actually been disproved that Quadrilateral  is a rectangle.


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Example question #4 : just how To find An angle In A Hexagon


True or false: every of the 6 angles that a continual hexagon measures 

*
.


Possible Answers:

True


False


Correct answer:

True


Explanation:

A continual polygon with 

*
 sides has 
*
 congruent angles, each of i beg your pardon measures 

*

Setting

*
, the common angle measure can be calculated come be

*

The statement is as such true.


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Example question #5 : how To uncover An angle In A Hexagon


True or false: each of the exterior angle of a continual hexagon measures

*
.


Possible Answers:

False


True


Correct answer:

False


Explanation:

If one exterior edge is bring away at every vertex of any kind of polygon, and their procedures are added, the sum is

*
. Every exterior edge of a constant hexagon has the very same measure, for this reason if us let
*
be that common measure, then

*

Solve because that

*
:

*

*

The statement is false.


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Example concern #6 : exactly how To discover An angle In A Hexagon


Given: Hexagon 

*
.

*

True, false, or undetermined: Hexagon 

*
 is regular.


Possible Answers:

Undetermined


True


False


Correct answer:

False


Explanation:

Suppose Hexagon 

*
 is regular. Each edge of a continual polygon of 
*
 sides has measure

*

A hexagon has 6 sides, therefore set 

*
; each angle that the continuous hexagon has actually measure

*

Since one angle is given to be of measure 

*
, the hexagon can not be regular.


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Example question #7 : how To discover An edge In A Hexagon


What is the measure of one exterior edge of a continuous twenty-sided polygon?


Possible Answers:
Correct answer:

*


Explanation:

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

*
. In a continuous polygon, the exterior angles all have actually the same measure, so division 360 by the number of angles, which, here, is 20, the same as the number of sides.

*
 


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Example question #8 : how To find An edge In A Hexagon


Which that the adhering to cannot be the six interior angle procedures of a hexagon?


Possible Answers:

All of these can be the six inner angle measures of a hexagon.


Correct answer:

All that these have the right to be the six interior angle steps of a hexagon.


Explanation:

The amount of the interior angle procedures of a hexagon is 

*

Add the angle actions in each group.

*

*

*

*

In each case, the edge measures include up come 720, therefore the answer is that all of these can be the six internal angle measures of a hexagon.

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