In the image provided, you have a pair of intersecting lines forming angles. The two labeled angles are:

• $2x^\circ$
• $(4x + 108)^\circ$

Since these angles are on a straight line and adjacent, they are supplementary, meaning their sum is 180°. We can set up the following equation:

$2x + (4x + 108) = 180$

Solve the equation:

1. Combine like terms: $6x + 108 = 180$

2. Subtract 108 from both sides: $6x = 72$

3. Divide both sides by 6: $x = 12$

Find each angle:

• The first angle is $2x$, so $2(12) = 24^\circ$.
• The second angle is $4x + 108$, so $4(12) + 108 = 48 + 108 = 156^\circ$.

Thus, the two angles are $24^\circ$ and $156^\circ$.

Would you like more details, or have any questions?

Here are 5 related questions to explore:

1. How do we know the angles are supplementary?
2. What if one of the angles were a right angle? How would the equation change?
3. Can you determine the vertical angles formed by this intersection?
4. What happens if $x$ is negative? Would the solution still work?
5. How would you solve this if both angles involved different terms of $x$?

Tip: Always remember that adjacent angles on a straight line sum to $180^\circ$.