SX¯¯¯¯¯¯¯¯ bisects <RST. m<RST = 10x. m<XST = 3x+16. Find m<RSX

Answer 1

Since SX bisects <RST, that means the angle <RST is divided into two congruent angles. Let's call the measure of each congruent angle y.

So we have:

<RST = y
<RSX = y
<XST = 3x + 16

Since the sum of the angles in a triangle is 180 degrees, we can write the equation:

<RST + <RSX + <XST = 180

Substituting the given values:

y + y + (3x + 16) = 180

Combining like terms:

2y + 3x + 16 = 180

Subtracting 16 from both sides:

2y + 3x = 164

Since <RST = y and its measure is 10x, we can write:

y = 10x

Substituting this into the previous equation:

2(10x) + 3x = 164

Simplifying:

20x + 3x = 164

Combining like terms:

23x = 164

Dividing both sides by 23:

x = 164/23

Simplifying:

x = 7.13

Now, let's find the measure of <RSX. We substitute this value of x back into the equation for <RSX:

<RST = 10x = 10(7.13) = 71.3 degrees

Therefore, m<RSX = 71.3 degrees.

Answer 2

The measure of two verticle angles are 9x + 3 and 12x - 6. Find x.(1 point) Responses

3

8.7

12

9.5

Answer 3

Vertically opposite angles are equal. Therefore, we can set up the equation:

9x + 3 = 12x - 6

To solve for x, we'll start by subtracting 9x from both sides:

3 = 3x - 6

Next, we'll add 6 to both sides:

9 = 3x

Finally, we'll divide both sides by 3:

3 = x

Therefore, the value of x is 3.

Answer 4

What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 3 is also divisible by 6. (1 point) Responses

12

26

9

30

Answer 5

A counterexample for the given conjecture would be a number that is divisible by 3 but not by 6.

So, the counterexample for the conjecture "Any number that is divisible by 3 is also divisible by 6" would be the number 9.

9 is divisible by 3, as \(9/3 = 3\), but it is not divisible by 6 since \(9/6 = 1.5\) which is not a whole number.