intermediate Geometry assist » airplane Geometry » Hexagons » just how to discover an edge in a hexagon

There is a regular hexagon v a side size of

. What is the measure of an internal angle?

Explanation:

Given the the hexagon is a consistent hexagon, this method that every the side size are congruent and all inner angles room congruent. The concern requires us to deal with for the measure of an inner angle. Offered the aforementioned meaning of a continual polygon, this means 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 deal with for the answer, the concern provides added information the isn"t necessarily required. The measure of an inner angle have the right to be fixed for using the equation:

where
is the number of sides of 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 edge In A Hexagon

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

Explanation:

The area has actually no relationship to uncover the edge of a constant hexagon.

There space 6 sides in a regular hexagon. Usage the adhering to formula to determine the inner angle.

Substitute

sides to determine the sum of all inner angles that the hexagon in degrees.

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

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

Given: consistent Hexagon

with center
. Build segments
and
to form Quadrilateral .

True or false: Quadrilateral

is a rectangle.

False

True

False

Explanation:

Below is regular Hexagon

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

Each edge of a constant hexagon measures

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

.

The angles of a rectangle must measure

, therefore it has been disproved that Quadrilateral  is a rectangle.

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

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

.

False

True

True

Explanation:

A continual polygon with

sides has
congruent angles, each of which measures

Setting

, the usual angle measure deserve to be calculated come be

The statement is as such true.

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

True or false: each of the exterior angles of a continuous hexagon measures

.

True

False

False

Explanation:

If one exterior edge is taken at each vertex of any polygon, and also their steps are added, the sum is

. Every exterior edge of a consistent hexagon has actually the same measure, therefore if us let
be that common measure, then

Solve because that

:

The declare is false.

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### Example inquiry #6 : just how To discover An edge In A Hexagon

Given: Hexagon

.

True, false, or undetermined: Hexagon

is regular.

False

True

Undetermined

False

Explanation:

Suppose Hexagon

is regular. Each edge of a constant polygon of
sides has actually measure

A hexagon has actually 6 sides, for this reason set

; every angle the the regular hexagon has measure

Since one angle is offered to it is in of measure

, the hexagon cannot be regular.

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### Example question #7 : exactly how To uncover An angle In A Hexagon

What is the measure up of one exterior angle of a regular twenty-sided polygon?

Explanation:

The sum of the exterior angle of any polygon, one at each vertex, is

. In a continuous polygon, the exterior angle all have actually the very same measure, so divide 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 : how To uncover An edge In A Hexagon

Which of the complying with cannot be the six interior angle steps of a hexagon?

All of these deserve to be the six interior angle steps of a hexagon.

All of these deserve to be the six interior angle procedures of a hexagon.

Explanation:

The amount of the interior angle procedures of a hexagon is

Add the angle procedures in every group.

In each case, the edge measures add up to 720, so the answer is that all of these can be the six interior angle steps of a hexagon.

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