The problem in the image shows two parallel lines (AB and CD) intersected by a transversal EF. The angles formed by the intersection of the lines and the transversal are labeled with algebraic expressions:

• $6x - 10^\circ$ at angle $\angle EHF$
• $4x - 2^\circ$ at angle $\angle CFP$

Given that AB and CD are parallel lines, corresponding angles are equal. Thus, $\angle EHF = \angle CFP$.

We can set up the equation:

$6x - 10 = 4x - 2$

Solving the equation:

$6x - 4x = -2 + 10$ $2x = 8$ $x = 4$

Now, substitute $x = 4$ back into the angle expressions:

• $\angle EHF = 6(4) - 10 = 24 - 10 = 14^\circ$
• $\angle CFP = 4(4) - 2 = 16 - 2 = 14^\circ$

Thus, both angles measure $14^\circ$.

Let me know if you need further details, or have any questions!

Relative Questions:

1. How can you verify that two angles are corresponding when a transversal crosses parallel lines?
2. What other types of angle relationships can be formed with parallel lines and a transversal?
3. How would the solution change if the lines were not parallel?
4. How do alternate interior angles differ from corresponding angles in this context?
5. What is the significance of parallel lines when solving equations involving angles?

Tip: Always look for equal corresponding or alternate angles when dealing with parallel lines and a transversal.