Question

the m∠2 = 55° and m∠6 = (3x - 2)°. find the vof x and m∠6.

Explanation:

Step1: Identify the relationship between ∠2 and ∠6

∠2 and ∠6 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal. So \(m\angle2 = m\angle6\).

Step2: Set up the equation

Since \(m\angle2 = 55^{\circ}\) and \(m\angle6=(3x - 2)^{\circ}\), we have the equation \(3x-2=55\).

Step3: Solve for \(x\)

Add 2 to both sides of the equation: \(3x-2 + 2=55 + 2\), which simplifies to \(3x=57\).
Divide both sides by 3: \(x=\frac{57}{3}=19\).

Step4: Find \(m\angle6\)

Substitute \(x = 19\) into the expression for \(m\angle6\). \(m\angle6=(3\times19 - 2)^{\circ}=(57 - 2)^{\circ}=55^{\circ}\).

Answer:

\(x = 19\), \(m\angle6=55^{\circ}\)