SX¯¯¯¯¯¯¯¯ bisects <RST. m<RST = 10x. m<XST = 3x+16. Find m<RSX
Since SX bisects <RST, m<RSX = m<SXT. We can set up an equation by setting m<RST equal to m<SXT:
10x = 3x + 16
Subtracting 3x from both sides:
7x = 16
Dividing both sides by 7:
x = 16/7
Now we can substitute this value of x back into the equation for m<RSX:
m<RSX = m<SXT = 3x + 16 = 3(16/7) + 16 = 48/7 + 112/7 = 160/7
Therefore, m<RSX is equal to 160/7.
To find the measure of angle RSX (m<RSX), we need to set up an equation based on the given information and solve for x.
Given:
m<RST = 10x
m<XST = 3x + 16
We know that angle RSX is bisected by line SX¯¯¯¯¯¯¯¯, so the measure of angle RSX (m<RSX) is equal to half the measure of angle RST (m<RST).
Since m<RST = 10x, we can set up the equation:
m<RSX = (1/2) * m<RST
Substituting the values given:
m<RSX = (1/2) * 10x
Now, we can substitute the value of m<XST into the equation:
(1/2) * 10x = 3x + 16
To solve for x, we can now simplify the equation:
5x = 3x + 16
Subtracting 3x from both sides:
5x - 3x = 3x - 3x + 16
2x = 16
Finally, we can solve for x by dividing both sides by 2:
2x/2 = 16/2
x = 8
Therefore, the value of x is 8.
To find the measure of angle RSX (m<RSX), substitute the value of x back into the equation:
m<RSX = (1/2) * 10x
m<RSX = (1/2) * 10(8)
m<RSX = (1/2) * 80
m<RSX = 40
So, the measure of angle RSX (m<RSX) is 40 degrees.
To find the measure of ∠RSX, we need to use the concept of angle bisectors.
Given that SX¯¯¯¯¯¯¯¯ bisects ∠RST, we know that ∠RSX is equal to ∠XSX¯¯¯¯¯.
We are given that the measure of ∠RST is 10x, and the measure of ∠XST is 3x + 16.
Since SX¯¯¯¯¯¯¯¯ bisects ∠RST, we can set up an equation:
∠RST = ∠XST
10x = 3x + 16
To solve for x, we need to isolate the variable.
First, subtract 3x from both sides of the equation:
10x - 3x = 3x + 16 - 3x
7x = 16
Then, divide both sides of the equation by 7:
7x/7 = 16/7
x = 16/7
Now that we have found the value of x, we can substitute it back into the equation to find the measure of ∠XSX¯¯¯¯¯:
∠XSX¯¯¯¯¯ = 3x + 16
∠XSX¯¯¯¯¯ = 3(16/7) + 16
Simplifying the expression:
∠XSX¯¯¯¯¯ = 48/7 + 16
∠XSX¯¯¯¯¯ = (48 + 112)/7
∠XSX¯¯¯¯¯ = 160/7
So, the measure of ∠XSX¯¯¯¯¯ is 160/7.
Since SX¯¯¯¯¯¯¯¯ bisects ∠RST, ∠RSX is equal to ∠XSX¯¯¯¯¯. Therefore, the measure of ∠RSX is also 160/7.