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q is equidistant from the sides of tsr. find rst. show work!

a.46

b.7

c.23

d.14

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

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