https://file.aiquickdraw.com/mathbot/file/1729161331090t25oervr.jpg

The problem states that:

- \( POQ \) is a straight line.
- \( \angle POR = 4x \)
- \( \angle QOR = 2x \)

Since \( POQ \) is a straight line, the sum of the angles on a straight line is \( 180^\circ \). Thus, we have the equation:

\[
\angle POR + \angle QOR = 180^\circ
\]

Substitute the given expressions for the angles:

\[
4x + 2x = 180^\circ
\]

Simplifying:

\[
6x = 180^\circ
\]

Now, solve for \( x \):

\[
x = \frac{180^\circ}{6} = 30^\circ
\]

So, the value of \( x \) is \( 30^\circ \).

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:
1. What would the value of \( \angle POR \) and \( \angle QOR \) be with \( x = 30^\circ \)?
2. How would the solution change if \( \angle POR \) was given as \( 3x \) instead of \( 4x \)?
3. What is the sum of angles around a point, and how does it differ from the sum of angles on a straight line?
4. Can you think of a scenario where the angles might form a triangle? What rules would apply?
5. How can you apply the linear pair angle concept in different geometric shapes?

**Tip:** Always remember that the sum of angles on a straight line is \( 180^\circ \), a useful fact for solving many geometry problems!

In figure, POQ is a line, ∠POR = 4x and ∠QOR = 2x. Find the value of x.

Solve a geometry problem where POQ is a straight line, and ∠POR = 4x and ∠QOR = 2x. Learn how to apply the linear pair theorem and the angle sum property to find the value of x, suitable for students in Grades 6-8.

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