https://file.aiquickdraw.com/mathbot/file/1726540227809xlf1383h.jpg

In this image, we are given a triangle with two marked angles: \( 45^\circ \) and an exterior angle of \( 110^\circ \). We are asked to find the angle \( x \) inside the triangle.

### Step-by-Step Solution:
1. **Use the Exterior Angle Theorem**: 
   The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle is \( 110^\circ \), and the non-adjacent interior angles are \( 45^\circ \) and \( x \).

   Therefore:
   \[
   110^\circ = 45^\circ + x
   \]

2. **Solve for \( x \)**:
   \[
   x = 110^\circ - 45^\circ = 65^\circ
   \]

Thus, the angle \( x \) is \( 65^\circ \).

Would you like more details on this, or do you have any questions?

### Additional Questions:
1. What is the sum of all interior angles in any triangle?
2. How can you calculate the third angle of a triangle if two angles are known?
3. How does the exterior angle theorem help in solving problems involving triangles?
4. What are some other ways to solve for unknown angles in triangles?
5. Can this problem be solved using other geometric theorems, like angle sums?

**Tip**: Remember that the sum of the interior angles of any triangle is always \( 180^\circ \), which can help solve various problems.

The angle x is degrees in a triangle with two known angles: 45° and an exterior angle of 110°.

This problem involves calculating the unknown interior angle x of a triangle using the exterior angle theorem. Given a triangle with angles 45° and an exterior angle of 110°, this step-by-step solution is suitable for students in Grades 7-9.

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