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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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3 years ago
Gabe went to the amusement park with $40 to spend. His ticket cost $26.50. Write and solve an inequality to show how much he mig
Goshia [24]
<h3><u>An inequality to show how much he might spend on souvenirs and snacks is:</u></h3>

x\leq 13.5

<h3><u>Solution:</u></h3>

Given that,

Gabe went to the amusement park with $40 to spend

His ticket cost $26.50

Therefore,

Total amount she has = $ 40

Ticket cost = $ 26.50

Let "x" be the amount he might spend on souvenirs and snacks

Therefore,

Remaining amount = 40 - 26.50

Remaining amount = 13.5

Thus she can spend less than or equal to $ 13.5 on souvenirs and snacks

Which is represented in inequality as:

x\leq 13.5

Thus the inequality is found

4 0
3 years ago
What’s the solution to this equation 2+x=7/8x-15
Nostrana [21]

Answer:x=−136

Step-by-step explanation: Step 1: Simplify both sides of the equation.

2+x=

7

8

x−15

2+x=

7

8

x+−15

x+2=

7

8

x−15

Step 2: Subtract 7/8x from both sides.

x+2−

7

8

x=

7

8

x−15−

7

8

x

1

8

x+2=−15

Step 3: Subtract 2 from both sides.

1

8

x+2−2=−15−2

1

8

x=−17

Step 4: Multiply both sides by 8.

8*(

1

8

x)=(8)*(−17)

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3 years ago
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Write an absolute value equation to satisfy the given solution set shown on a number line.
balandron [24]

The absolute value equation with the wanted solutions is:

|x| - 1/2 = 0

<h3>How to find the absolute value equation?</h3>

Here we want to find an absolute value equation such that the solutions are:

x = -1/2 and x = 1/2.

Remember that the absolute value equation always changes the sign, such that the outcome is positive.

This means that:

|1/2| = 1/2

|-1/2| = 1/2

Then a trivial equation with these two solutions is:

|x| - 1/2 = 0

Where the two solutions are x = 1/2 and x = -1/2.

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