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°.