Question

Q is equidistant from the sides of ∠TSR Find m∠RST The diagram is not to scale.

Answer 1

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