Question

find the value of x for which r || s. then find m∠1 and m∠2.
m∠1 = 72 - 2x
m∠2 = 84 - 3x
the value of x for which r || s is □.

Explanation:

Step1: Use the property of parallel lines

When \(r\parallel s\), \(\angle1\) and \(\angle2\) are equal (corresponding angles). So, \(72 - 2x=84 - 3x\).

Step2: Solve the equation for \(x\)

Add \(3x\) to both sides: \(72 - 2x+3x=84 - 3x+3x\), which simplifies to \(72 + x=84\).
Subtract \(72\) from both sides: \(x=84 - 72\).

Answer:

\(x = 12\)