https://file.aiquickdraw.com/mathbot/file/1726698930978o4esdz2n.jpg

To solve for \( x \) in the given diagram, we need to analyze the angles.

### Step 1: Use the property of angles on a straight line
The sum of angles on a straight line is always 180°. In the diagram, the angles on the straight line are:
- \( 108^\circ \) on the left
- An unknown angle adjacent to \( x^\circ \)
- \( 30^\circ \) on the right

Thus, the unknown angle adjacent to \( x \) (which I'll call \( \alpha \)) can be found as:
\[
\alpha = 180^\circ - (108^\circ + 30^\circ) = 180^\circ - 138^\circ = 42^\circ
\]

### Step 2: Apply the triangle sum property
In a triangle, the sum of all interior angles is always 180°. In the triangle formed by the angles \( x^\circ \), \( 40^\circ \), and \( \alpha \), we know that:
\[
x^\circ + 40^\circ + 42^\circ = 180^\circ
\]

Solving for \( x \):
\[
x = 180^\circ - (40^\circ + 42^\circ) = 180^\circ - 82^\circ = 98^\circ
\]

Thus, \( x = 98^\circ \).

Would you like further details or have any questions?

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Here are five related questions:
1. What is the sum of interior angles in a triangle?
2. How do we calculate the exterior angle of a triangle?
3. Can you explain how angles on a straight line sum up to 180°?
4. What is the role of alternate interior angles in parallel lines?
5. How can we calculate the missing angle in a right triangle?

**Tip**: When working with geometric figures, always look for supplementary angles on a straight line and the sum of angles within a triangle.

Find x in a triangle with angles 40°, x, and an exterior angle 108° adjacent to a 30° angle on a straight line.

Learn how to solve for x in a triangle using the triangle sum theorem and the property of angles on a straight line. This problem involves calculating interior and exterior angles. Suitable for students in Grades 6-8.

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