40

120

60

150

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.

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

The value of x is equal to

Step-by-step explanation:

we know that

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

where

n is the number of sides of the polygon

In this problem

substitute

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

In this problem

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

where

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

n is the number of sides

In this problem we have

substitute in the formula

therefore

the answer Part 1) is

the sum of the interior angle measures of a 20-gon is

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

where

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

n is the number of sides

In this problem we have

substitute in the formula

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

so

therefore

the answer Part 2) is

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

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 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 sides

therefore

The answer Part 4) is

the measure of an exterior angle of a regular octagon is

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 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

therefore

the answer part 5) is

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

where

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

n is the number of sides

In this problem we have

substitute in the formula

therefore

the answer Part 1) is

the sum of the interior angle measures of a 20-gon is

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

where

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

n is the number of sides

In this problem we have

substitute in the formula

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

so

therefore

the answer Part 2) is

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

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 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 sides

therefore

The answer Part 4) is

the measure of an exterior angle of a regular octagon is

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 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

therefore

the answer part 5) is

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

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