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Tatiana [17]
3 years ago
14

Find the measure of an interior angle and exterior angle of a regular 24gon

Mathematics
1 answer:
Julli [10]3 years ago
8 0

Answer:

Interior Angle: 165°

Exterior Angle: 15°

Step-by-step explanation:

So first you have to find the sum of all interior angles of a polygon with <u>24 sides</u>. This can be found using the formula:

sum = ( <em>n</em> - 2 ) * 180°     where '<em>n</em>' is the number of sides.

When '<em>n</em> = 24' then the sum is:

sum = ( 24 - 2 ) * 180°

Simplify and solve.

sum = 22 * 180°

sum = 3960°

Since there are 24 sides to the polygon, there are 24 interior angles. <u>Assuming that this polygon is equilateral</u>, you can surmise that:

<em>Interior Angle</em> = sum° / <em>n</em>   where n is the number of sides,

3960° / 24 = 165° = Interior Angle

Using that information, and combine it with the [Supplementary Angles Theorem] the exterior angle can be found by:

165° + x = 180°

Solve for x.

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Find the sum (x^3+5x^2+3x-7)+(8x-6^2+6) <br> Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)
KATRIN_1 [288]

Answer:

x^3 - x^2 + 11x - 1

-x^3 - 8x^2 + 5x + 7

Step-by-step explanation:

Find the sum

(x^3+5x^2+3x-7)+(8x-6x^2+6)

=x^3+5x^2+3x-7+8x-6x^+6

Collect like terms

=x^3 +5x^2-6x^2+3x+8x-7+6

Add the like terms

= x^3 - x^2 + 11x - 1

Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)

(7x-3x^2+2)-(x^3+5x^2+2x-5)

= 7x-3x^2+2-x^3-5x^2-2x+5

Collect like terms

= -x^3-3x^2-5x^2+7x-2x+2+5

Add the like terms

= -x^3 - 8x^2 + 5x + 7

5 0
3 years ago
How do you solve this
Fed [463]

Answer:

x is equal to 55 degrees.

Step-by-step explanation:

In order to find this, we must first realize that the angle next to 160 is equal to 20 degrees. This is because they come together to make a straight line, which is equal to 180 degrees.

Now knowing this, we can find the two congruent angles at the top. Since they form one angle of a large triangle along with the right angle and 20 degrees, we know they combine to be worth 70 degrees. Since they are even, we know each is 35 degrees.

For the final step, we know that the 35 degree angle and 90 degree angle form a triangle with x. Knowing these all add up to 180, we can solve for x.

35 + 90 + x = 180

125 + x = 180

x = 55

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4 years ago
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3 years ago
On Saturday, Nicole earns no more than $55 at her job. On Sunday, she earns at least $40. Which of these inequalities represent
makkiz [27]

Answer:

B

Step-by-step explanation:

use your head

7 0
3 years ago
Read 2 more answers
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