**Which equation can be used to solve for \[x\] in the following diagram?**

\[3x^\circ\]\[(8x -20)^\circ~~\]

Choose 1 answer:

Choose 1 answer:

(Choice A)   

\[3x + (8x - 20) = 90\]

A

\[3x + (8x - 20) = 90\]

(Choice B)   

\[3x = (8x - 20)
\]

B

\[3x = (8x - 20)
\]

(Choice C)   

\[3x + 90 = (8x - 20)\]

C

\[3x + 90 = (8x - 20)\]

(Choice D)   

\[3x + (8x - 20) = 180\]

D

\[3x + (8x - 20) = 180\]

The diagram seems to show two angles that are either adjacent (forming a straight line) or complementary. Since we're asked to choose an equation that relates these angles, let's consider the possibilities.

Given:
- One angle is \(3x^\circ\).
- The other angle is \((8x - 20)^\circ\).

Now let's analyze the choices:

- **If the two angles are adjacent and form a straight line**, they should add up to \(180^\circ\).

The correct equation would then be:
\[
3x + (8x - 20) = 180
\]

So, the correct answer is:

**Choice D:** \(\boxed{3x + (8x - 20) = 180}\)

Would you like to see how to solve this equation for \(x\)? Here are 5 related questions:

1. How do you solve \(3x + (8x - 20) = 180\) for \(x\)?
2. What are adjacent angles, and how do they relate to a straight line?
3. What is the relationship between supplementary angles?
4. How would the equation change if the angles were complementary instead of forming a straight line?
5. Can you verify the solution by substituting \(x\) back into the original angles?

**Tip:** When two angles are on a straight line, they are supplementary and their sum is always \(180^\circ\).

Learn how to solve for x in a geometry problem involving angle relationships. Understand the application of the Angle Sum Theorem and solve the equation step-by-step. Suitable for students in Grades 7-9.

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