Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. What figure did he draw

By using proportion, the value of x is,

⇒ x = 30

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

the pair of polygons is similar.

Hence, By using proportion we get;

⇒ 30/12 = 75/x

Solve for x by cross multiply,

⇒ x = 75 x 12 / 30

⇒ x = 30

Thus, By using proportion, the value of x is,

⇒ x = 30

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Answer:

a. 1 =ST; 20 = RS;5 = x

b. 40 = ST; 20 = RS; 12 = x

c.17 = RT;6 = RS; 7 = x

d. 34 = RT; 15 = RS; 6 = x

Step-by-step explanation:

___

Since the exercise ONLY tells you that PointSis inbetweenRT,use the SegmentAdditionPostulate for all exercises:

d.8x - 14 = 19 + [4x - 9]

8x - 14 = 10+ 4x(Combine like-terms)

- 8x-8x

___________________

-14 = 10 - 4x

-10-10

_____________

-24 = -4x

________

-4-4

6 = x[Plug this back into the equations above to get these measures: 34 = RT; 15 =RS]

c.x+ 10 = 11 + [2x - 8]

x+10 = 3+ 2x(Combine like-terms)

-2x-2x

________________

-x + 10 = 3

- 10-10

___________

-x= -7

____

-1-1

x = 7 [Plug this back into the equations above to get these measures: 17 = RT; 6 = RS]

b.60 = [4x - 8] + [3x - 16]

60 = 7x-24(Combine like-terms)

+24+ 24

______________

84 = 7x

______

77

12 = x[Plug this back into the equations above to get these measures: 40 = ST; 20 = RS]

a.21 = [x - 4] + [2x + 10]

21 = 3x+6(Combine like-terms)

-6- 6

______________

15 = 3x

______

33

5 = x[Plug this back into the equations above to get these measures: 1 = ST; 20 = RS]

I am delighted to assist you anytime.

To solve for x and find the lengths RS, ST, and RT, we can set up an equation using the given information. Using the equation RS + ST + RT = 0 and substituting the given values, we can simplify the equation to find x. With the value of x, we can then find the lengths RS, ST, and RT. Therefore, RS = -8, ST = -13, and RT = 21.

To write an equation in terms of x, we need to set up an equation using the given information RS = 2x + 10, ST = x - 4, and RT = 21.

We can start by writing the equation RS + ST + RT = 0.

Substituting the given values, we get (2x + 10) + (x - 4) + 21 = 0. Simplifying this equation, we have 3x + 27 = 0.

Solving for x, we subtract 27 from both sides and divide by 3, to get x = -9.

With the value of x, we can now find the lengths RS, ST, and RT. RS = 2(-9) + 10 = -8, ST = (-9) - 4 = -13, and RT = 21.

Therefore, RS = -8, ST = -13, and RT = 21.

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