exterior is 76 and inside angle of a triangle is 52 what is x

In any triangle, the exterior angle is equal to the sum of the two non-adjacent interior angles.

Given that:
- The exterior angle is \(76^\circ\),
- One of the interior angles is \(52^\circ\).

Let \(x\) represent the other non-adjacent interior angle.

By the exterior angle theorem:
\[
76^\circ = 52^\circ + x
\]

Solving for \(x\):
\[
x = 76^\circ - 52^\circ = 24^\circ
\]

Thus, \(x = 24^\circ\).

Would you like further explanation or clarification?

Here are five related questions to expand your understanding:
1. How do you calculate the exterior angle of a polygon?
2. What is the sum of all interior angles in a triangle?
3. Can a triangle have more than one exterior angle?
4. How can the exterior angle theorem help solve unknown angles in a triangle?
5. What is the relationship between the interior and exterior angles of a polygon?

**Tip**: Always remember that the sum of the interior angles of a triangle is \(180^\circ\).

Discover how to calculate the unknown angle in a triangle when given an exterior angle of 76° and one interior angle of 52°. This problem involves key geometric concepts, including the exterior angle theorem. Ideal for students in Grades 6-8.

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