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

There is a continuous hexagon through a side length of

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


*


*


*


*


Explanation:

Given that the hexagon is a regular hexagon, this way that all the side size are congruent and also all internal angles space congruent. The concern requires us to settle for the measure up of an inner angle. Offered the aforementioned definition of a continuous polygon, this way that there should only it is in one correct answer.

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

In bespeak to solve for the answer, the inquiry provides extr information the isn"t necessarily required. The measure up of an inner angle have the right to be resolved for utilizing the equation:

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

In this case,

*
.

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

*

*

*

*


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Example question #2 : how To discover An angle In A Hexagon


What is the internal angle of a regular hexagon if the area is 15?


Possible Answers:
Correct answer:

*


Explanation:

The area has no relevance to uncover the edge of a consistent hexagon.

There space 6 political parties in a constant hexagon. Usage the following formula to identify the interior angle.

*

Substitute 

*
 sides to identify the amount of all interior angles of the hexagon in degrees.

*

Since there are 6 sides, divide this number by 6 to recognize the worth of each internal angle.

*


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Example question #3 : how To uncover An angle In A Hexagon


Given: continuous Hexagon 

*
 with center 
*
. Build segments 
*
 and 
*
 to kind Quadrilateral .

True or false: Quadrilateral 

*
 is a rectangle.


Possible Answers:

False


True


Correct answer:

False


Explanation:

Below is regular Hexagon 

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

*

Each angle of a continual hexagon measures 

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

*
.

The angles of a rectangle must measure 

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


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Example inquiry #4 : just how To discover An edge In A Hexagon


True or false: every of the six angles the a consistent hexagon measures 

*
.


Possible Answers:

False


True


Correct answer:

True


Explanation:

A continual polygon with 

*
 sides has 
*
 congruent angles, every of i m sorry measures 

*

Setting

*
, the common angle measure deserve to be calculated come be

*

The statement is as such true.


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Example concern #5 : just how To find An angle In A Hexagon


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

*
.


Possible Answers:

True


False


Correct answer:

False


Explanation:

If one exterior edge is bring away at each vertex of any polygon, and their actions are added, the sum is

*
. Each exterior angle of a constant hexagon has actually the exact same measure, for this reason if us let
*
be that common measure, then

*

Solve because that

*
:

*

*

The declare is false.


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Example question #6 : exactly how To uncover An angle In A Hexagon


Given: Hexagon 

*
.

*

True, false, or undetermined: Hexagon 

*
 is regular.


Possible Answers:

False


True


Undetermined


Correct answer:

False


Explanation:

Suppose Hexagon 

*
 is regular. Each angle of a regular polygon of 
*
 sides has measure

*

A hexagon has actually 6 sides, so set 

*
; each angle of the consistent hexagon has measure

*

Since one angle is offered to it is in of measure 

*
, the hexagon cannot be regular.


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Example concern #7 : exactly how To discover An angle 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 type of polygon, one at each vertex, is 

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

*
 


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Example inquiry #8 : just how To find An angle In A Hexagon


Which of the following cannot be the six interior angle measures of a hexagon?


Possible Answers:

All that these can be the six internal angle actions of a hexagon.


Correct answer:

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


Explanation:

The amount of the internal angle measures of a hexagon is 

*

Add the angle actions in every group.

*

*

*

*

In every case, the edge measures include up come 720, so the prize is that all of these deserve to be the six interior angle steps of a hexagon.

See more: D Is Sugar Dissolving In Water A Physical Change Or, Why Is Sugar In Water A Physical Change

 

 

 


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