What is the number of sides of a regular polygon if each interior angle measures 160°?

Given:

The vertices of the quadrilateral ABCD are A(3,8), B(6,5), C(5,4), and D(2,7).

To find:

Whether the given quadrilateral is a rectangle, a rhombus or a square.

Solution:

Distance formula: The distance between two points is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, the side lengths are:

[tex]AB=\sqrt{\left(6-3\right)^2+\left(5-8\right)^2}[/tex]

[tex]AB=\sqrt{\left(3\right)^2+\left(-3\right)^2}[/tex]

[tex]AB=\sqrt{9+9}[/tex]

[tex]AB=\sqrt{18}[/tex]

[tex]AB=3\sqrt{2}[/tex]

Similarly,

[tex]BC=\sqrt{\left(5-6\right)^2+\left(4-5\right)^2}=\sqrt{2}[/tex]

[tex]CD=\sqrt{\left(2-5\right)^2+\left(7-4\right)^2}=3\sqrt{2}[/tex]

[tex]AD=\sqrt{\left(2-3\right)^2+\left(7-8\right)^2}=\sqrt{2}[/tex]

The length  of diagonals are:

[tex]AC=\sqrt{\left(5-3\right)^2+\left(4-8\right)^2}=2\sqrt{5}[/tex]

[tex]BD=\sqrt{\left(2-6\right)^2+\left(7-5\right)^2}=2\sqrt{5}[/tex]

From the above calculation, we conclude that the given quadrilateral has two pairs of congruent opposite sides and equal diagonals.

Opposite sides of a rectangle are equal and its diagonals are also equal.

Therefore, the given quadrilateral ABCD is a rectangle.

Step-by-step explanation:

y=x+7........eqni

y=6x+2.....eqnii

putting the value of x in eqnii

y=6x+2

or, x+7=6x+2

or, 7-2=6x-x

or 5= 5x

hence,x=1

sbstutuung the value of x in eqni,

y= x+7

=1+7

=8

hence the value of y is 8

Answer:

m=76

Step-by-step explanation:

Answer:

B

C

D

Step-by-step explanation:

Answer:

B, C, D

Step-by-step explanation:

One major arc is Arc G H E.

Arc FE is a minor arc.

The measure of Arc F E is 41°.

Answer:

100 x 4 = 400 - 91 = 309

Step-by-step explanation:

Answer:

100= 4 + 3 (100-1)

4+3 (99)

4 + 297 is 301

Step-by-step explanation:

The first row starts with 4 toothpicks, and they increase by +3 in each row.  The first tree is already accounted for which makes the 4 + 3, and why I have 100-1.  The teacher said the answer was correct but I doubted the equation.  Can you tell me if this is correct?

Answer: 1/2+11/3 = 4.1*6

Step-by-step explanation:

Answer:

1 5/6

Step-by-step explanation:

2 and 3 both have an LCM of 6, so in order to combine them you have to make the denominators 6. To do that, you multiply 1/2 by 3, and 1/3 by 2. When you do that, you get 3/6 and 1 2/6. When you add those, you get 1 5/6.

Answer:

Y = [tex]\frac{-3}{2}[/tex] x + 4

Step-by-step explanation:

Answer:

y=-3x+6

Step-by-step explanation:

Answer:

7 1/24

Step-by-step explanation:

I) Use common denominator:

8 x 3 = 6 x 4 = 24

9 7/8 = 9 21/24

2 5/6 = 2 20/24

II) Subtract:

9 21/24 - 2 20/24 = 7 1/24

Answer:

(8 + 24) ÷ (12 x 4)

Step-by-step explanation:

Answer:

(8 + 24)  ÷ ( 12 x 4 )

Step-by-step explanation:

32 / 48 = 2/3

Answer:

The answer is 6

Step-by-step explanation:

Answer:

The Area of the given figure is 6 inch²

Step-by-step explanation:

For a given Trapezoid

side a = 1 ½ = 1.5 inch

side b = 2½ = 2.5 inch

height (h) = 3 inch

Now, Area of Trapezoid

A = ½ (a + b) × h

A = ½ (1.5 + 2.5) × 3 inch

A = ½ × 4 × 3 inch

A = 2 × 3 inch

A = 6 inch²

Thus, The Area of the given figure is 6 inch²

-TheUnknownScientist

Answer:

7.35

Step-by-step explanation:

5 pounds -> 5.25

1 pound -> 1.05

7 pounds-> 7.35

Answer: Y-5= Dawn age

Step-by-step explanation:

Answer:

y=3x+1

Step-by-step explanation:

x is the weeks and y is the final product

Answer:

1+(3x7) she has 22 dollars

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The system of equations can be written ...

  n + d = 20 . . . . . . . . coins in the jar

  5n +10d = 130 . . . . . value in cents

_____

Using the first equation, we can write an expression for n:

  n = 20 -d

We can substitute this into the second equation:

  5(20 -d) +10d = 130

  100 +5d = 130 . . . . . . simplify

  5d = 30 . . . . . . . . . . . . subtract 100

  d = 6 . . . . . . . . . . . . divide by 5

  n = 20-d = 14

The jar contains 14 nickels and 6 dimes.

Answer:

21

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 1/8 yards

Answer: 4,896 + 480 = 5376

Step-by-step explanation:

Answer:

480 = small rectangular prism on right Rectangle on left = 4896 so                480 + 4896 = 5376

Answer: i think its 7 cm pretty sure

Answer:

D

Step-by-step explanation:

Inequalities of the type have | x | > a have solutions of the form

x < - a , x > a

Thus

| x | > 11

x < - 11 and x > 11

Answer:

75

Step-by-step explanation:

Look for where the line passes through the y-axis. If the line doesn't go through the y-axis, like in this case, look for where the line starts on the y-axis.

yes i think because i think so

Answer:

Yes

Step-by-step explanation:

Their sides are similar proportionally and the 60 degrees + 120 degrees makes 180 degrees meaning the OTHER angles match

Answer:

The answer is 3/100 I hope this helps :)

Step-by-step explanation:

the answer is 3/100

B is equivalent to the equation

Answer:

x=0 and y= -2

Step-by-step explanation:

−5x+y=−2for y:

−5x+y=−2

−5x+y+5x=−2+5x(Add 5x to both sides)

y=5x−2

5x−2foryin−3x+6y=−12:

−3x+6y=−12

−3x+6(5x−2)=−12

27x−12=−12(Simplify both sides of the equation)

27x−12+12=−12+12(Add 12 to both sides)

27x=0

x=0

Substitute0 for X in y=5x−2:

y=5x−2

y=(5)(0)−2

y=−2(Simplify both sides of the equation)

Answer:

0dh 8/6

Step-by-step explanation:

Answer:

-8/27

Step-by-step explanation:

First, make all fractions an improper fraction.

-2/3 / 9/4

Flip the right fraction over.

-2/3 * 4/9

multiply

and you get -8/27