Question

if the m∠2 is 60°, what is the m∠6?
question 6
solve for x.

Explanation:

Step1: Identify angle - relationship

If the lines \(l\) and \(m\) are parallel, \(\angle2\) and \(\angle6\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.

Step2: Determine the measure of \(\angle6\)

Since \(\angle2 = 60^{\circ}\) and \(\angle2\) and \(\angle6\) are corresponding angles, \(m\angle6=m\angle2\). So \(m\angle6 = 60^{\circ}\).

for second - part:

Step1: Set up the equation

The two angles \((4x + 2)^{\circ}\) and \((7x-20)^{\circ}\) are either vertical angles (equal) or supplementary angles (sum to \(180^{\circ}\)). Assuming they are vertical angles (since no information about parallel lines is given to suggest they are supplementary in a different way), we set up the equation \(4x + 2=7x-20\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(2 = 7x-4x-20\), which simplifies to \(2 = 3x-20\).
Add \(20\) to both sides: \(2 + 20=3x\), so \(22 = 3x\).
Divide both sides by \(3\): \(x=\frac{22}{3}\)

Answer:

\(60^{\circ}\)