SX¯¯¯¯¯¯¯¯ bisects <RST. m<RST = 10x. m<XST = 3x+16. Find m<RSX(
Since SX bisects angle RST, we know that m<RST = m<RXS.
Therefore, m<RXS = 10x.
Since m<XST = 3x + 16, and m<RST = 10x, we can set up an equation:
3x + 16 = 10x
Subtract 3x from both sides:
16 = 7x
Divide both sides by 7:
2.286 = x
Now substitute this value back into m<RXS = 10x:
m<RXS = 10(2.286)
m<RXS ≈ 22.86
So, m<RSX ≈ m<RXS ≈ 22.86.
To find the measure of ∠RSX, we need to use the given information about the angles ∠RST and ∠XST.
Given:
m∠RST = 10x
m∠XST = 3x + 16
Since SX¯¯¯¯¯¯¯¯ bisects ∠RST, it means that ∠RSX and ∠XST are equal.
So, we can equate the expressions for these two angles:
10x = 3x + 16
To solve for x, we can subtract 3x from both sides of the equation:
10x - 3x = 3x + 16 - 3x
7x = 16
Now, divide both sides of the equation by 7 to isolate x:
x = 16/7
To find the measure of ∠RSX, substitute the value of x back into the expression:
m∠RSX = 10x
m∠RSX = 10 * (16/7)
Simplifying this expression:
m∠RSX = 160/7
Therefore, the measure of ∠RSX is 160/7.
To find the measure of angle RSX, we need to determine the values of x, which we can then use to calculate the measure of the angle.
In the given problem, we are told that SX¯¯¯¯¯¯¯¯ bisects angle RST, which means that it divides the angle into two equal angles. Therefore, m<RSX and m<XST must be equal.
We are given that m<RST = 10x and m<XST = 3x + 16. Since m<XST = m<RSX, we can equate these two measures to get:
3x + 16 = 10x
To solve for x, we'll subtract 3x from both sides:
16 = 10x - 3x
Combining like terms:
16 = 7x
Next, divide both sides of the equation by 7:
16/7 = x
Now, we know that x = 16/7.
To find the measure of angle RSX, substitute this value of x back into one of the given angle measures. Let's use m<XST = 3x + 16:
m<RSX = m<XST = 3(16/7) + 16
Now, simplify this expression:
m<RSX = 48/7 + 16
To add these fractions, we need a common denominator which is 7:
m<RSX = (48 + 112)/7
m<RSX = 160/7
Therefore, the measure of angle RSX is 160/7.