- AAn interior angle of a regular polygon can never be larger than 150°
- BThe matching exterior angle is 25°, and 360° is not exactly divisible by 25°
- CThe interior angle of a regular polygon must always be a whole multiple of 30°
- DAn exterior angle as small as 25° is below the smallest one that any regular polygon can have
Step-by-Step Solution
At each vertex the interior and exterior angles are supplementary, so the exterior angle would be 180° − 155° = 25°. The exterior angles of any polygon add to exactly 360°, so a regular n-sided polygon needs 360/n = 25, giving n = 14.4 — not a whole number, so no such polygon exists. The other explanations are all false: a regular 24-gon has interior angles of 165°, well above 150°; a regular pentagon has 108°, which is no multiple of 30°; and exterior angles can be made as small as one likes by taking enough sides, a regular 360-gon having exterior angles of 1°.
Answer: B) The matching exterior angle is 25°, and 360° is not exactly divisible by 25°