Question

r is between h and z. hr = x - 2, hz = 13, and rz = x + 7. draw and label the segment. x= hr=

Explanation:

Step1: Use segment - addition postulate

Since R is between H and Z, we have $HR + RZ=HZ$. Substitute the given expressions: $(x - 2)+(x + 7)=13$.

Step2: Simplify the left - hand side

Combine like terms: $x-2+x + 7=2x+5$. So, $2x + 5=13$.

Step3: Solve for x

Subtract 5 from both sides: $2x=13 - 5=8$. Then divide both sides by 2: $x = 4$.

Step4: Find HR

Substitute $x = 4$ into the expression for HR. $HR=x - 2$. So, $HR=4-2=2$.

Answer:

$x = 4$
$HR=2$