If the exterior angle Y measures 117°, the sum of angles X and Z would be ______ degrees.

The sum of angles \( X \) and \( Z \) would be **63 degrees**.

Here’s why:

In any triangle, an exterior angle is equal to the sum of the two opposite interior angles. Therefore,
\[
X + Z = Y.
\]
Given that \( Y = 117^\circ \), we have:
\[
X + Z = 180^\circ - 117^\circ = 63^\circ.
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is the formula for finding an exterior angle in a polygon?
2. How do you determine the sum of interior angles in a triangle?
3. Can a triangle have more than one exterior angle equal to 117°?
4. How does the sum of exterior angles change with different polygons?
5. How can this concept be applied to quadrilaterals?

**Tip:** Remember, for any triangle, the sum of its interior angles is always 180°.

Discover how to find the sum of angles X and Z in a triangle when the exterior angle Y is 117°. This problem illustrates the Exterior Angle Theorem, showing that the sum of two opposite interior angles equals the exterior angle. Ideal for students in Grades 6-8.

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