m<RSX = degrees (Type the number ONLY)
bisects <RST. m<RST = 10x. m<XST = 3x+16. Find m<RSX(2 points) ¯ S
To find m<RSX, we need to find the value of x first.
Since RSX bisects RST, we know that m<RST = 2 * m<RSX. So, we can write the equation as:
10x = 2 * (3x + 16)
Simplifying the equation:
10x = 6x + 32
Subtracting 6x from both sides:
4x = 32
Dividing both sides by 4:
x = 8
Now that we have the value of x, we can find m<RSX:
m<RSX = 2 * (3x + 16)
m<RSX = 2 * (3 * 8 + 16)
m<RSX = 2 * (24 + 16)
m<RSX = 2 * 40
m<RSX = 80
Therefore, m<RSX is 80 degrees.
To find the value of m<RSX, we need to find the value of x first, and then we can substitute it into the given expression to find m<RSX.
Given:
m<RST = 10x
m<XST = 3x + 16
It is also given that <RSX bisects <RST, which means the measures of <RSX and <SXT are equal.
Let's set up an equation using the information given:
m<RST = m<SXT
Since <RSX bisects <RST, it means that the sum of m<RST and m<SXT is equal to m<RSX.
So, we can write:
10x + (3x + 16) = m<RSX
Simplifying:
13x + 16 = m<RSX
Therefore, m<RSX = 13x + 16.
To find the measure of angle RSX, we need to use the angles formed by the bisector.
Given:
m<RST = 10x
m<XST = 3x + 16
Since the angle RSX is bisected by line segment RX, we can use the angle bisector theorem to find the measure of RSX.
According to the angle bisector theorem, the ratio of the lengths of the two segments formed by an angle bisector is equal to the ratio of the measures of the two angles created by the bisector.
In this case, we have RS and XS as the two segments formed by bisector RX, and we want to find the measure of angle RSX.
To find the ratio, we need to set up an equation.
The ratio can be expressed as:
RS / XS = m<RST / m<XST
Substituting the given measures:
RS / XS = 10x / (3x + 16)
We can cross-multiply to solve for RS:
RS * (3x + 16) = XS * 10x
Expand the equation:
3x * RS + 16 * RS = 10x * XS
Now, we need to use the fact that RS + XS = 180 degrees, as they form a straight line, to further simplify the equation.
RS + XS = 180
RS = 180 - XS
Substitute the value of RS in the previous equation:
3x * (180 - XS) + 16 * (180 - XS) = 10x * XS
Simplify the equation:
540x - 3x * XS + 2880 - 16 * XS = 10x * XS
Now, collect all the terms involving XS on one side:
-3x * XS - 10x * XS + 16 * XS = -540x + 2880
Factor out XS:
XS * (-3x - 10x + 16) = -540x + 2880
Combine terms:
XS * (3x - 16) = -540x + 2880
Divide both sides by (3x - 16):
XS = (-540x + 2880) / (3x - 16)
Now we have the value of XS. We can substitute this back into the equation RS = 180 - XS to find the value of RS.
RS = 180 - (-540x + 2880) / (3x - 16)
Simplify the equation to find RS.
Once we know the values of RS and XS, we can substitute them into the equation
m<RSX = m<RST - m<XST.
m<RSX = 10x - (3x + 16).
Simplify the equation to find the measure of angle RSX.
After calculating the value for x, substitute it into m<RSX = 10x - (3x + 16) to find the measure of angle RSX.