Which of the following expressions represents an exterior angle of triangle $XYZ$?

• A. $\alpha +\beta$
• B. $\beta +\gamma$
• C. $\alpha +\beta +\gamma$
• D. $\alpha +\gamma$

Answer: (A)

Verified step by step guidance

1. Recall that an exterior angle of a triangle is formed by extending one side of the triangle and measuring the angle between this extended side and the adjacent side of the triangle.
2. Understand the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
3. Identify the interior angles of triangle XYZ as \( \alpha \), \( \beta \), and \( \gamma \). If you extend a side at vertex corresponding to angle \( \gamma \), the exterior angle formed will be equal to \( \alpha + \beta \).
4. Analyze each given expression to see which one matches the sum of two interior angles that are not adjacent to the exterior angle: \( \alpha + \beta \), \( \beta + \gamma \), \( \alpha + \beta + \gamma \), and \( \alpha + \gamma \).
5. Conclude that the correct expression representing an exterior angle of triangle XYZ is the sum of the two interior angles not adjacent to the exterior angle, which is \( \alpha + \beta \).