The answer is A. (42)
WORKINGS
Since Q is equidistant from the sides of ∠TSR,
∠TSQ = ∠QSR
m∠TSQ = 4x + 5
m∠QSR = 8x – 11
Therefore, 4x + 5 = 8x – 11
Solving for x
4x + 5 = 8x – 11
Add 11 to both sides of the equation
4x + 5 + 11 = 8x – 11
+ 11
4x + 16 = 8x
Subtract 4x from both sides of the equation
4x + 16 – 4x = 8x – 4x
16 = 4x
4x = 16
x = 16/4
x = 4
∠RST is the same as ∠TSR
m∠RST = ∠TSQ + ∠QSR
m∠RST = 4x + 5 + 8x – 11
m∠RST = 12x – 6
m∠RST = (12 x 4) – 6
m∠RST = 48 – 6
m∠RST = 42 degrees
