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Tatiana [17]
2 years ago
14

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

Mathematics
1 answer:
Julli [10]2 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
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(3,−2), B(6, -2), C(6, 5) D
Vikki [24]

Answer:

Step-by-step explanation:

Distance=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}} \\

A(3,-2) ;  B(6,-2)

AB=\sqrt{(6-3)^{2}+(-2-[-2])^{2}}\\\\ =\sqrt{3^{2}+(-2+2)^{2}}\\\\=\sqrt{9+0}=\sqrt{9}\\\\

AB = 3 units

B(6,-2) ;  C(6,5)

BC=\sqrt{(6-6)^{2}+(5-[-2])^{2}} \\\\=\sqrt{0+(5+2)^{2}}\\\\=\sqrt{(7)^{2}}\\

BC = 7 units

Area of rectangle = length * width

                             = AB * BC

                             = 3 * 7

                             = 21 square units

3 0
3 years ago
Read 2 more answers
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of
Lubov Fominskaja [6]

<u>Answer:</u>

First car:  35 gallons

Second car: 15 gallons

<u>Step-by-step explanation:</u>

Assuming x to be the gas consumed by 1st car and 50 - x to be the gas consumed by 2nd car.

We know that:

Distance traveled = fuel efficiency × gas consumed

20x+35(50-x)=1225

20x+1750-35x=1225

35x-20x=1750-1225

15x=525

x=35

So 50 - x = 50-35=15

Therefore, first car consumed 35 gallons while second car consumed 15 gallons.

7 0
3 years ago
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Please help no links!
slavikrds [6]

Answer:

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Step-by-step explanation:

7 0
2 years ago
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Instructions: state what additional information is required in order to know that the triangle in the image below are congruent
Dafna1 [17]

Answer:

QP ≈ HG

Common side between those angles are QP and HG

so, they should be congruent to prove AAS

Answered by GAUTHMATH

8 0
2 years ago
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