https://file.aiquickdraw.com/mathbot/file/17298218871590rcfg2ra.jpg

In this image, we see a geometric figure consisting of two angles, \( 31^\circ \) and \( 107^\circ \), and the unknown angle \( x^\circ \). 

The key observation is that these three angles are around a straight line. This means we can apply the **angle on a straight line rule**, which states that the sum of angles around a straight line is \( 180^\circ \).

The sum of the angles \( 31^\circ \), \( 107^\circ \), and \( x^\circ \) should be \( 180^\circ \). Thus, we can set up the following equation:

\[
31^\circ + 107^\circ + x^\circ = 180^\circ
\]

Simplifying:

\[
138^\circ + x^\circ = 180^\circ
\]

Solving for \( x \):

\[
x^\circ = 180^\circ - 138^\circ = 42^\circ
\]

Thus, the value of \( x \) is \( \boxed{42^\circ} \).

Would you like any additional details or have questions on how this was solved?

Here are 5 related questions for further practice:

1. What is the sum of the interior angles of a triangle?
2. If two angles on a straight line are \( 72^\circ \) and \( x^\circ \), what is \( x \)?
3. How do you calculate the exterior angle of a triangle?
4. What is the supplementary angle to \( 58^\circ \)?
5. How do you identify adjacent angles on a straight line?

**Tip:** Angles on a straight line always add up to \( 180^\circ \). Keep this in mind when working with geometric figures!

Find the value of x in the given geometric figure with angles 31°, 107°, and x° on a straight line.

Learn how to find the value of x in a geometric problem where the angles are 31°, 107°, and x°. This problem involves using the sum of angles on a straight line to solve for the unknown angle. Suitable for students in Grades 6-8.

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