Question

1. if a || b and m∠1 = 4x - 1 and m∠2 = 6x - 11 find the measure of ∠1 ?

Explanation:

Step1: Use property of parallel lines

Since \(a\parallel b\), \(\angle1\) and \(\angle2\) are alternate - interior angles, so \(m\angle1 = m\angle2\). Then we set up the equation \(4x - 1=6x - 11\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(-1 = 6x-4x - 11\), which simplifies to \(-1 = 2x - 11\). Then add 11 to both sides: \(2x=10\), and divide by 2 to get \(x = 5\).

Step3: Find the measure of \(\angle1\)

Substitute \(x = 5\) into the expression for \(m\angle1\), \(m\angle1=4x - 1=4\times5 - 1=19\).

Answer:

\(19\)