Mathematics - Sequence & Series Question with Solution | TestHub

Let the first (smallest) angle be $a$. Then $a+(n-1)4^{\circ }=172^{\circ }$, so $a=172^{\circ }-4^{\circ }(n-1)$. Sum of interior angles: $\frac{n}{2}\left[a+172^{\circ }\right]=(n-2)180^{\circ }$. Substituting $a:\frac{n}{2}\left[2\times 172^{\circ }-4^{\circ }(n-1)\right]=(n-2)180^{\circ }$. Simplifying: $86n-n^2+n=90n-180$, so $n^2+3n-180=0,(n+15)(n-12)=0,n=12$.