https://file.aiquickdraw.com/mathbot/file/172677053894000uj0vb2.jpg

In the image, you are tasked with finding the value of \( y \), which is part of a triangle and a linear pair involving an exterior angle. Here’s the step-by-step breakdown:

1. **Triangle Angle Sum Property**: 
   The sum of the angles in any triangle is always \( 180^\circ \). The given angles inside the triangle are \( 47^\circ \) and \( 41^\circ \).

   \[
   \text{Remaining angle in the triangle} = 180^\circ - (47^\circ + 41^\circ) = 180^\circ - 88^\circ = 92^\circ
   \]

2. **Exterior Angle Theorem**: 
   The exterior angle \( y \) is supplementary to the \( 92^\circ \) angle inside the triangle since they form a linear pair. Thus:

   \[
   y + 92^\circ = 180^\circ
   \]
   \[
   y = 180^\circ - 92^\circ = 88^\circ
   \]

Therefore, the value of \( y \) is \( 88^\circ \).

Do you have any questions or would you like further details?

Here are five related questions for further exploration:
1. How do you calculate the exterior angle of a triangle?
2. What is the sum of interior angles of a triangle?
3. How can you use the supplementary angle property in different geometric problems?
4. How would you solve for the other angles if the triangle was non-right-angled and obtuse?
5. Can the exterior angle be greater than \( 180^\circ \) in any geometric figure?

**Tip**: Remember that the exterior angle theorem states that an exterior angle of a triangle equals the sum of the two non-adjacent interior angles.

Find the value of y in the triangle, where the internal angles are 47° and 41°, and the external angle y is formed by a linear pair with one of the triangle's angles.

Learn how to calculate the external angle y in a triangle where the internal angles are 47° and 41°. This problem demonstrates the Triangle Angle Sum Property and the Exterior Angle Theorem, suitable for Grades 6-9.

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