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The problem involves an exterior angle of a triangle, which is given as \( 74^\circ \). The exterior angle theorem tells us that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

In the diagram:
- One of the opposite interior angles is \( 24^\circ \).
- The other interior angle is \( x^\circ \).

So, we can set up the following equation:

\[
74^\circ = 24^\circ + x^\circ
\]

Now, solving for \( x \):

\[
x = 74^\circ - 24^\circ = 50^\circ
\]

Thus, the value of \( x \) is \( 50^\circ \).

Would you like more details or have any questions about this solution?

Here are some related questions for further practice:
1. What is the sum of the interior angles of a triangle?
2. How does the exterior angle theorem relate to the interior angles of a triangle?
3. Can a triangle have more than one exterior angle at a vertex?
4. What happens to the exterior angle when the triangle is equilateral?
5. How do you find the missing angle in a triangle given two interior angles?

**Tip:** Always remember that the exterior angle of a triangle equals the sum of the two non-adjacent interior angles!

A side of the triangle below has been extended to form an exterior angle of 74°. Find the value of x.

Learn how to apply the Exterior Angle Theorem to find the missing angle x in a triangle where one of the exterior angles is 74°. The solution involves adding the two opposite interior angles. Suitable for students in Grades 6-8.

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