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In this problem, you're asked to find the value of \( x \), which is an interior angle of a triangle, and you're given an exterior angle of \( 157^\circ \) along with another interior angle of \( 109^\circ \).

### Steps to solve:

1. **Exterior Angle Theorem**: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the exterior angle is \( 157^\circ \), and the two non-adjacent interior angles are \( x^\circ \) and \( 109^\circ \).

   So, the relation is:
   \[
   157^\circ = x^\circ + 109^\circ
   \]

2. **Solving for \( x \)**:
   \[
   x = 157^\circ - 109^\circ
   \]
   \[
   x = 48^\circ
   \]

Thus, the value of \( x \) is \( \boxed{48^\circ} \).

Would you like more details on this? Here are some related questions you might want to explore:

1. What is the sum of the interior angles of any triangle?
2. How does the exterior angle theorem apply to all types of triangles?
3. What are the properties of supplementary angles in geometry?
4. How can the exterior angle theorem be used in real-world scenarios?
5. What are other methods to solve for unknown angles in a triangle?

**Tip**: The exterior angle theorem is a powerful tool that works for all triangles, regardless of their type (scalene, isosceles, or equilateral).

A side of the triangle has been extended to form an exterior angle of 157°. Find the value of x given that another interior angle is 109°.

Solve a triangle problem where an exterior angle of 157° is given, and an interior angle is 109°. Learn how to apply the exterior angle theorem to find the missing angle x in this geometry problem. Suitable for students in Grades 7-9.

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