Question

1. determine the value of x for which r || s if

• m∠1 = 20 - 8x; and
• m∠2 = 30 - 16x.

20
0.75
1.25
10

Explanation:

Step1: Use the property of parallel lines

When \(r\parallel s\), \(\angle1\) and \(\angle2\) are congruent (alternate - interior angles). So, \(m\angle1 = m\angle2\).

Step2: Set up the equation

Substitute the given expressions for \(m\angle1\) and \(m\angle2\):
\(20 - 8x=30 - 16x\)

Step3: Solve for \(x\)

Add \(16x\) to both sides of the equation:
\(20 - 8x+16x=30 - 16x+16x\)
\(20 + 8x=30\)
Subtract \(20\) from both sides:
\(20-20 + 8x=30 - 20\)
\(8x = 10\)
Divide both sides by \(8\):
\(x=\frac{10}{8}=\frac{5}{4}=1.25\)

Answer:

\(1.25\)