If the polygon in the previous problem is a **regular** decagon, what is the measure of each interior angle?
A$180^{\circ}$
B$144^{\circ}$
C$135^{\circ}$
D$108^{\circ}$
Answer & Solution
Correct answer: B. $144^{\circ}$
A regular polygon has all interior angles equal, so each equals the total divided by $n$:
Each interior angle $= \dfrac{1{,}440^{\circ}}{10} = 144^{\circ}$.
- Trap A ($108$) is the regular pentagon's interior angle.
- Trap B ($135$) is the regular octagon's.
- Trap D ($180$) is a straight angle, not the interior angle of any closed polygon.
General formula: each interior angle of a regular $n$-gon $= \dfrac{(n-2) \cdot 180^{\circ}}{n}$.
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