Question

1. if qr = 8x + 1 and qs = 20x - 26, then rs = ?

Explanation:

Step1: Recognize segment - addition postulate

Since point $R$ lies on line segment $QS$, we have $QR + RS=QS$.

Step2: Substitute expressions

Substitute $QR = 8x + 1$ and $QS=20x - 26$ and $RS$ (which we want to find) into the equation: $(8x + 1)+RS=20x - 26$. Then, $RS=20x - 26-(8x + 1)$.

Step3: Simplify the right - hand side

$RS=20x - 26 - 8x-1$. Combine like terms: $RS=(20x - 8x)+(-26 - 1)$. So, $RS = 12x-27$.

Step4: Solve for $x$

Since we know that $QR = RS$ (from the congruence marks on the figure), we set $8x + 1=12x-27$.
Subtract $8x$ from both sides: $1 = 12x-8x-27$.
$1 = 4x-27$.
Add 27 to both sides: $4x=1 + 27$.
$4x=28$.
Divide both sides by 4: $x = 7$.

Step5: Find $RS$

Substitute $x = 7$ into the expression for $RS$: $RS=12x-27$.
$RS=12\times7-27$.
$RS = 84 - 27$.
$RS = 57$.

Answer:

$57$