Find the value of the variable x in the following proportions

6/x = 9/8
x=48/9=5.333333...

5/5 = 4/x
x=4

1/2 = 2/x
x=4

x/10 = 10/8
x=12.5

Are my answers correct?

Yes! They are all correct.

Thank you for checking them! :D

You're welcome.

if the angle of a regular polygon measures 16 4/11 how many sides does it have?

Let's evaluate each proportion to check if your answers are correct.

1. 6/x = 9/8
To solve for x, we can cross-multiply: 6 * 8 = 9 * x
48 = 9x
Dividing both sides of the equation by 9 will give us: x = 48/9 = 5.33333...
Your answer is correct.

2. 5/5 = 4/x
Here, we can simply simplify the left side of the equation: 5/5 = 1
The equation becomes 1 = 4/x
To isolate x, we can cross-multiply: 1 * x = 4 * 1
x = 4
Your answer is correct.

3. 1/2 = 2/x
To solve for x, we can cross-multiply: 1 * x = 2 * 2
x = 4
Your answer is correct.

4. x/10 = 10/8
To solve for x, we need to cross-multiply: x * 8 = 10 * 10
8x = 100
Dividing both sides of the equation by 8 will give us: x = 100/8 = 12.5
Your answer is correct.

Therefore, all of your answers are correct. Well done!