ANSWER: A. 46
SOLUTION
Given that Q is equidistant from the sides of TSR
m∠TSQ = m ∠QSR
To solve for x
m∠TSQ = 3x + 2
m ∠QSR = 8x – 33
Since m∠TSQ = m ∠QSR
3x + 2 = 8x – 33
Add 33 to both sides
3x + 2 + 33 = 8x – 33 + 33
3x + 35 = 8x
8x = 3x + 35
Subtract 3x from both sides
8x – 3x = 3x – 3x + 35
5x = 35
Divide both sides by 5
x = 7
Since m∠TSQ = 3x + 2, and x = 7
m∠TSQ = (3*7) + 2
m∠TSQ = 21 + 2
m∠TSQ = 23
To solve for RST
Given that Q is equidistant from the sides of RST
m∠RST = m∠TSQ + m ∠QSR
Since m∠TSQ = m ∠QSR
m∠RST = 2m∠TSQ = 2m ∠QSR
Ginen, m∠RST = 2m∠TSQ
m∠TSQ = 23
m∠RST = 2(23)
m∠RST = 46