Discussion
If one internal angle of a regular polygon is 135°, then the number of diagonals in the polygon is :
Answer: B
The polygon has 20 diagonals.
An interior angle of 135° means an exterior angle of 45°, and the exterior angles add up to 360°:
\[ \begin{aligned} n &= \frac{360}{45} = 8 \\ \text{Diagonals} &= \frac{n(n - 3)}{2} = \frac{8 \times 5}{2} = 20 \end{aligned} \]
The polygon is a regular octagon. None of 15, 18 and 25 is the number of diagonals of any polygon: the counts for 3 to 9 sides run 0, 2, 5, 9, 14, 20, 27.
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