What's the GCF of 20, 28, 24

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

2 years ago

The mean age of Mr Jasmi,Miss Haslinda and their three children is 38 years. The mean age of their three children is 18 years. C

DedPeter [7]

Answer: 68

Explanation:

Let x be the age of Mr Jasmi
y be the age of Miss Haslinda
a + b + c be the age of the 3 children

We can write:
(x + y + a + b + c)/5 = 38

But:
(a + b + c)/3 = 18
a + b + c = 18(3)
a + b + c = 54

Substitute this value to our first equation

(x + y + 54)/5 = 38
x + y + 54 = 38(5)
x + y + 54 = 190
x + y = 190 - 54
x + y = 136

Thus:
Mean age of (mr jasmi and miss Linda) = (x+y)/2

But x + y = 136

=> mean age = 136/2 = 68

4 0

2 years ago

Explain how u subtract 247 from 538

VashaNatasha [74]

247- 538 = -291
If you line them up in that order 247 you'll have to borrow. Your answer would be -291
-538

The only way to not get -291 is to flip the two numbers.

6 0

3 years ago

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Please help me. this is hard

allochka39001 [22]

Since it is a square that means each side is equal.
The perimeter is 24, and since there is four sides we would divide it by four to find the length of each side.

24/4 = 6

Each side is 6.
By looking at the picture, one side of the square, is the length of the radius.

The radius of the square is 6.

The only thing left to do is to find the circumference.
The circumference formulas are:

C = $\pi$ d
C = 2 $\pi$ r

We can use the first one Diameter x pi (3.14)
To find the diameter we would just multiply the radius by two.

6 x 2 = 12

Diameter = 12

So multiply it by pi

12 x 3.14 = 37.68
or D 12 $\pi$

7 0

3 years ago

If one pound is the same weight as 16 ounces, how many ounces equal 3.5 pounds? (only input whole numbers.)

astra-53 [7]

Answer: well 56 is the answer

Step-by-step explanation:

5 0

2 years ago

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