Question

which angle is an exterior angle?
\\(\angle z\\)
\\(\angle x\\)
\\(\angle y\\)
\\(\angle w\\)

Explanation:

Define an exterior angle of a polygon

An exterior angle of a polygon is formed by one side of the polygon and the extension of an adjacent side. It must form a linear pair with the adjacent interior angle.

Analyze each labeled angle

• \(\angle x\): This is an interior angle of the pentagon.
• \(\angle w\): This is a reflex angle on the outside, but it is not formed by extending a side; it spans the outer non-adjacent region.
• \(\angle z\): This angle is formed between an extended side and another line, but it is not a proper linear pair with the interior angle.
• \(\angle y\): This angle is formed by one side of the pentagon and the extension of the adjacent top-right side, forming a linear pair with the interior angle.

Identify the correct option

Therefore, \(\angle y\) is the exterior angle.

Answer:

• \(\angle z\)
• \(\angle x\)
• \(\angle y\) (Correct answer)
• \(\angle w\)