https://file.aiquickdraw.com/mathbot/file/1727238808146re0itfu9.jpg

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 \( 180^\circ \).

What are the values of the angles in the image with the equations 2x° and (4x + 108)°?

This solution explains how to find the angles in a geometry problem involving the equations 2x° and (4x + 108)° using the supplementary angles theorem. Learn how to set up and solve the equation step by step, suitable for students in Grades 7-9.

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