Question

1. if ro = 5x and rq = 12x - 20, find the value of x. then find ro, oq, and rq.

in exercises 51 and 52, identify the segment bisector of $overline{st}$. then find st.
7.
8.
x + 12 8x - 2
2x + 3 4x - 7
s m t
s m t

Explanation:

Step1: Assume RO = RQ (assuming some equal - length condition not shown in problem statement but common in segment - related problems)

$5x=12x - 20$

Step2: Move like terms to one side

$20=12x - 5x$

Step3: Simplify the right - hand side

$20 = 7x$

Step4: Solve for x

$x=\frac{20}{7}$

Now find RO, OQ and RQ:

Step5: Find RO

$RO = 5x=5\times\frac{20}{7}=\frac{100}{7}$

Step6: Find RQ

$RQ = 12x-20=12\times\frac{20}{7}-20=\frac{240}{7}-\frac{140}{7}=\frac{100}{7}$

Step7: Find OQ

Since RO = RQ, OQ = 0

Answer:

$x=\frac{20}{7}$, $RO=\frac{100}{7}$, $OQ = 0$, $RQ=\frac{100}{7}$