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 $-1 = 2x-11$. Add 11 to both sides: $-1 + 11=2x$, so $10 = 2x$. Divide both sides by 2, we get $x = 5$.

Step3: Find the measure of $\angle1$

Substitute $x = 5$ into the expression for $m\angle1$. $m\angle1=4x - 1=4\times5 - 1=20 - 1 = 19$.

Answer:

$19$