Practice free →
HomeGRE › Quantitative Reasoning › If the polygon in the previous problem is a **re…

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 $= \dfrac{(n-2) \cdot 180^{\circ}}{n}$.
Solve this in the app — GRE practice & 24k+ MCQs →
Related questions