SX bisects <RST.
m<RST = 10x. m<XST = 3x+16. Find m<RSX(2 points)
m<RSX = degrees (Type the number ONLY)
To find m<RSX, we need to use the fact that SX bisects <RST.
Since SX bisects the angle, the measure of <RSX is equal to half the measure of <RST.
Given that m<RST = 10x, we can write the equation:
m<RSX = 1/2 * m<RST
Substituting the value of m<RST, we have:
m<RSX = 1/2 * 10x
m<RSX = 5x
Therefore, m<RSX = 5x degrees.
To find the measure of angle RSX, we can use the fact that SX bisects angle RST.
By the Angle Bisector Theorem, we know that the measure of angle RSX is given by:
m<RSX = (m<RST)/(m<RST + m<XST) * m<XST
Plugging in the given values, we have:
m<RSX = (10x)/(10x + 3x + 16) * (3x + 16)
Simplifying this expression, we have:
m<RSX = (10x)/(13x + 16) * (3x + 16)
Multiplying the terms, we have:
m<RSX = (30x^2 + 160x)/(13x + 16)
Therefore, the measure of angle RSX is:
m<RSX = 30x^2 + 160x / 13x + 16
To find the measure of angle RSX, we can use the fact that angle SX bisects angle RST.
Since angle SX bisects angle RST, the measure of RST can be expressed as twice the measure of RSX. Let's denote the measure of RSX as y.
So, we have:
m<RST = 10x
m<RSX = y
m<XST = 3x + 16
From the given information, we can set up the equation:
10x = 2y (angle SX bisects angle RST)
3x + 16 = y (angle SX bisects angle XST)
We can solve this system of equations to find the value of y.
Solving the first equation for x, we get:
x = (2y) / 10 = y / 5
Now, we substitute this value of x into the second equation:
3(y / 5) + 16 = y
Multiplying through by 5 to clear the fraction:
3y + 80 = 5y
Rearranging the equation:
2y = 80
Dividing by 2:
y = 40
Therefore, the measure of angle RSX is 40 degrees.