https://file.aiquickdraw.com/mathbot/file/1729207252114depz6wb8.jpg

In this diagram, we see two angles, \(125^\circ\) and \(130^\circ\), along with an unknown angle \(x^\circ\), which appears at the vertex where the two lines meet.

This setup is based on the concept of the "exterior angle theorem." The sum of the interior angles on one side of a straight line is always \(180^\circ\). Here, the sum of the three angles must equal \(360^\circ\), because they form a complete revolution around a point.

We can set up the equation as:
\[
125^\circ + 130^\circ + x^\circ = 360^\circ
\]
Now, solving for \(x^\circ\):
\[
x^\circ = 360^\circ - (125^\circ + 130^\circ)
\]
\[
x^\circ = 360^\circ - 255^\circ = 105^\circ
\]

So, \(x = 105^\circ\).

Would you like further details or clarifications on this? Here are five related questions to expand on this concept:

1. What is the exterior angle theorem and how does it apply here?
2. How do you calculate the sum of angles around a point?
3. What would happen if the sum of angles exceeded 360 degrees?
4. Can you apply this method to other geometric shapes, such as triangles?
5. How can you determine angles in parallel line configurations?

**Tip:** Always remember that angles around a point sum up to 360°, and for any straight line, adjacent angles sum up to 180°.

In the diagram, find the unknown angle x when the two given angles are 125° and 130°.

Solve the geometry problem by finding the unknown angle x in a diagram where two angles are 125° and 130°. This solution involves the exterior angle theorem and understanding the sum of angles around a point. Suitable for Grades 7-9 students.

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