Exercise 2 Page 350

Examining the given diagram, we can see that ∠ PQS and ∠ SQR are adjacent congruent angles. This means that QS forms a bisector of ∠ PQR.

According to the Angle Bisector Theorem, if a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle. Therefore, PS=RS. This allows us to write an equation. PS=RS ⇒ 6x+5=9x-4 Let's solve it.

6x+5=9x-4

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Solve for x

SubEqn

LHS-6x=RHS-6x

5=3x-4

AddEqn

LHS+4=RHS+4

9=3x

DivEqn

.LHS /3.=.RHS /3.

3=x

RearrangeEqn

Rearrange equation

x=3

Once we know the value of x, let's substitute it to the expression of RS. 9x-4 → 9( 3)-4 → 23 Therefore, RS=23.