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The diagram shows a triangle with one exterior angle labeled as \(x^\circ\) and an interior angle of \(40^\circ\). There is also another interior angle, though its measurement is not directly given.

To solve for \(x^\circ\), we can apply the exterior angle theorem, which states that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

Let the unknown angle in the triangle be labeled as \(y^\circ\).

- The sum of the interior angles in a triangle is always \(180^\circ\). Thus, for this triangle, we can write:
  \[
  y^\circ + 40^\circ + \text{third angle} = 180^\circ
  \]

The third angle is the one adjacent to \(x^\circ\), so:
  \[
  x^\circ = 40^\circ + y^\circ
  \]

Now we know that \(x^\circ = 180^\circ - (\text{third angle})\). Since it is likely meant to be an isosceles or equilateral shape based on the arrow and layout

In the diagram, find the value of the exterior angle labeled as x° based on the given interior angles (one of which is 40°).

This problem involves applying the Exterior Angle Theorem to find the value of an exterior angle in a triangle. One of the interior angles is given as 40°, and the solution provides a detailed step-by-step explanation. Suitable for students in Grades 6-8.

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