Ray QS bisects <PQR. Solve for X and find m<PQR
m<PQR= x+3
m<PQS= 4x- 14
can someone help me set up this problem and how to solve it?
1/2 (x+3) = 4x - 14
x + 3 = 8x - 28
31 = 7x
x = 31/7
angle PQR = x + 3 = 31/7 + 3 = 52/7
angle PQS = 4(31/7) - 14 = 26/7 , which is half of 52/7
showing my answer is correct
4 x - 14 = (1/2) (x+3)
8 x - 28 = x + 3
7 x = 31
x = 31/28
sorry 31/7
To solve this problem, we can set up an equation based on the given information and use algebraic methods to solve for the unknown variable, x.
Given:
m<PQR = x + 3
m<PQS = 4x - 14
Since ray QS bisects angle <PQR, it means that m<PQS and m<PQR are equal. Hence, we can equate the two angles:
4x - 14 = x + 3
Now, we can solve this equation to find the value of x.
1. Start by simplifying the equation. To do this, we can subtract x from both sides of the equation:
4x - x - 14 = 3
This simplifies to:
3x - 14 = 3
2. Next, isolate the variable term by adding 14 to both sides of the equation:
3x - 14 + 14 = 3 + 14
This simplifies to:
3x = 17
3. To solve for x, divide both sides of the equation by 3:
(3x) / 3 = 17 / 3
This simplifies to:
x = 17 / 3
Now that we have the value of x, we can substitute it back into one of the given equations to find the measure of angle <PQR.
Using the equation:
m<PQR = x + 3
Substituting x = 17/3, we get:
m<PQR = 17/3 + 3
To simplify this expression, you can find a common denominator and then add the fractions:
m<PQR = (17 + 9) / 3
m<PQR = 26 / 3
Therefore, the measure of angle <PQR is 26/3.