What is the value of x in the regular polygon below?
40
120
60
150


What is the value of x in the regular polygon below?  40 120 60 150

Answers

Answers
Question 1) =3240o
Question 2) =150o
Question 3) = There is no diagram given
Question 4) = 450
Question 5) = 15 sides.

Explanation
The formula for getting the sum of interior angle is,
Sn=90(2n-4)
Where Sn = sum of regular interior angle of n sides.
n = number of sides
Question 1)
S20=90(2×20-4)
=90 ×36
=3240
Question 2)
Sn=90(2×12-4)
=90×20
=1800
one interior angle=1800/12=150
Question 3)
No diagram given
Question 4)
The sum of exterior angles of a regular polygon = 360.

360÷8=45
answer= 〖45〗^o
Question 5)
The sum of exterior angles of a regular polygon = 360.
360÷24=15
15 sides. 

x=40

Step-by-step explanation:

The ploygon has 6 sides.  The sum of the interior angles  of a polygon with n sides is (n – 2)180.

(6-2) *180

4*180 = 720

The total of the sum of the angles is 720

We have 6 interior angles of 3x

6*3x = 720

18x = 720

Divide each side by 18

18x/18 = 720/18

x=40

x = √3

A complete question related to this found on chegg is stated below:

A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x​ . (Hint: A regular hexagon can be divided into six congruent triangles.)

Find attached the diagram.

Step-by-step explanation:

Side length = 1cm

A regular hexagon has six equal the side length. A line drawn from the center to any vertex will have the same length as any side.

This implies the radius is equal to the side length.

As a result, when lines are drawn from the center to each of the vertex, a

regular hexagon is said to be made of six equilateral triangles.

From the diagram, x = 2× apothem

Apothem is the distance from the center of a regular polygon to the midpoint of a side.

Using Pythagoras theorem, we would get the apothem

Hypotenuse ² = opposite ² + adjacent²

1² = apothem² + (½)²

Apothem = √(1² -(½)²)

= √(1-¼) = √¾

Apothem = ½√3

x = 2× Apothem = 2 × ½√3

x = √3


A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x​ . (Hi
A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x​ . (Hi

The value of x is equal to 40\°

Step-by-step explanation:

we know that

The sum of the internal angles of a polygon is equal to

S=(n-2)180\°

where

n is the number of sides of the polygon

In this problem

n=6\ sides

substitute

S=(6-2)180\°=720\°

To find the measure of one internal angle of the figure, divide the sum by the number of sides

720\°/6=120\°

In this problem

3x=120\°

x=120\°/3=40\°

The answer to your question is 90°

Step-by-step explanation:

Process

1.- Calculate the sum of the internal angles in a triangle

Formula = 180(N - 2)

N = 6

              = 180(6 - 2)

              = 180(4)

              = 720° and each angle measures    720/6

                                                                                      = 120°

2.- Calculate the value of the internal angles of the triangle

In the triangle, one angle measures 120° and the other two measures

    180 - 120 = 60° but these angles are equal because the triangle is isosceles.

    Then each small angle in the triangle measures 30°

3.- Calculate x

    x = 120 - 30

    x = 90°

Part 1) What is the sum of the interior angle measures of a 20-gon?

we know that

The formula for getting the sum of interior angle is equal to

S=180*(n-2)

where

S is the sum of the interior angles of a regular polygon.

n is the number of sides

In this problem we have

n=20\ sides

substitute in the formula

S=180*(20-2)

S=180*(18)=3,240\°

therefore

the answer Part 1) is

the sum of the interior angle measures of a 20-gon is 3,240\°

Part 2) What is the measure of one interior angle of a regular 12-gon?

The formula for getting the sum of interior angle is equal to

S=180*(n-2)

where

S is the sum of the interior angles of a regular polygon.

n is the number of sides

In this problem we have

n=12\ sides

substitute in the formula

S=180*(12-2)

S=180*(10)=1,800\°

Divide the sum of the interior angles by the number of sides to obtain the measure of one interior angle

so

1,800\°/12=150\°

therefore

the answer Part 2) is

the measure of one interior angle of a regular 12-gon is 150\°

Part 3) No diagram given

Part 4) What is the measure of an exterior angle of a regular octagon?

we know that

The sum of exterior angles of a regular polygon is equal to  360 degrees

so

Divide the sum of exterior angles by the number of sides to obtain the measure of one exterior angle

the regular octagon has 8 sides

360\°/8=45\°

therefore

The answer Part 4) is

the measure of an exterior angle of a regular octagon is 45\°

Part 5) If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?

we know that

The sum of exterior angles of a regular polygon is equal to  360 degrees

so

Divide the sum of exterior angles by the measure of an exterior angle to obtain the number of sides of the regular polygon

360\°/24\°=15\ sides

therefore

the answer part 5) is

15\ sides

Part 1) What is the sum of the interior angle measures of a 20-gon?

we know that

The formula for getting the sum of interior angle is equal to

S=180*(n-2)

where

S is the sum of the interior angles of a regular polygon.

n is the number of sides

In this problem we have

n=20\ sides

substitute in the formula

S=180*(20-2)

S=180*(18)=3,240\°

therefore

the answer Part 1) is

the sum of the interior angle measures of a 20-gon is 3,240\°

Part 2) What is the measure of one interior angle of a regular 12-gon?

The formula for getting the sum of interior angle is equal to

S=180*(n-2)

where

S is the sum of the interior angles of a regular polygon.

n is the number of sides

In this problem we have

n=12\ sides

substitute in the formula

S=180*(12-2)

S=180*(10)=1,800\°

Divide the sum of the interior angles by the number of sides to obtain the measure of one interior angle

so

1,800\°/12=150\°

therefore

the answer Part 2) is

the measure of one interior angle of a regular 12-gon is 150\°

Part 3) No diagram given

Part 4) What is the measure of an exterior angle of a regular octagon?

we know that

The sum of exterior angles of a regular polygon is equal to  360 degrees

so

Divide the sum of exterior angles by the number of sides to obtain the measure of one exterior angle

the regular octagon has 8 sides

360\°/8=45\°

therefore

The answer Part 4) is

the measure of an exterior angle of a regular octagon is 45\°

Part 5) If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?

we know that

The sum of exterior angles of a regular polygon is equal to  360 degrees

so

Divide the sum of exterior angles by the measure of an exterior angle to obtain the number of sides of the regular polygon

360\°/24\°=15\ sides

therefore

the answer part 5) is

15\ sides

im pretty sure that its 40

Step-by-step explanation:

A

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6, thus

sum = 180° × 4 = 720°

Thus each interior angle = 720° ÷ 6 = 120° and therefore

3x = 120 ( divide both sides by 3 )

x = 40 → A

The correct answer is A. 40

Step-by-step explanation:

Let's recall that the sum of the six interior angles of an hexagon add up to 720°, therefore, every angle is 120 degrees.

Now we can solve for x, this way:

3x = 120

x = 120/3

x = 40

The correct answer is A. 40



Do you know the answer?

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