Given that the two arcs have the given points as endpoints), the angle of intersection of these two arcs is at least $\left(1-\frac{2}{n}\right) \pi$.

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Given that the two arcs have the given points as endpoints), the angle of intersection of these two arcs is at least $\left(1-\frac{2}{n}\right) \pi$.
7. Let $P_{1}, P_{3}$ be points in the polygon $E$. The line $P_{1} P_{2}$ intersects the boundary of $E$ at $Q_{1}, Q_{2}$. If $Q_{1}, Q_{2}$ can be transformed by two similar transformations to make $a_{1}^{\prime}, a_{1}^{\prime}$ into the arcs $\alpha_{1}, a_{2}$ connecting $P_{1}$ and $P_{3}$, and the angles at which they intersect at $P_{1}, P_{2}$ are the same as the angles at which $\boldsymbol{a}_{1}^{\prime}, a_{2}^{\prime}$ intersect at $Q_{1}, Q_{2}$. Thus, we only need to discuss the case where the given two points are on the boundary.

Let $Q_{1}, Q_{3}$ be two endpoints of $E$. By performing two similar or translational transformations on the incircle of $E$, we can obtain two arcs inside $E$ connecting $Q_{1}, Q_{2}$ (when $Q_{1}, Q_{2}$ are endpoints of a side of $E$, one is an arc, and the other is the side $Q_{1} Q_{2}$ of $E$), which are tangent to the sides of $E$ with endpoints $Q_{1}, Q_{2}$.

If $Q_{1}$ is a vertex and $Q_{2}$ is on the side $V_{2} V_{3}$. Perform two (usually different) similar transformations with $Q_{1}$ as the center of homothety, transforming the arcs connecting $Q_{1}, V_{1}$ and $Q_{1}, V_{3}$ into arcs connecting $Q_{1}$ and $Q_{2}$. These arcs are still tangent to the sides of $E$ passing through $Q_{1}$, and their intersection angle remains $\left(1-\frac{2}{n}\right) \pi$.

If $Q_{1}, Q_{2}$ are on the sides $V_{1} V_{2}, V_{1} V_{1+1}$ respectively, use a pair of arcs to connect $V_{1}, Q_{1}$ and a pair of arcs to connect $V_{2}, Q_{2}$, with each pair of arcs intersecting at an angle of $\left(1-\frac{2}{n}\right) \pi$. Among these arcs, two intersect the line $Q_{1} Q_{2}$ at another point outside $E$, and the angle at which these two arcs intersect at $Q_{1}$ is $\geqslant\left(1-\frac{2}{n}\right) \pi$. Using $Q_{2}$ as the center, perform two similar transformations to transform these two arcs into another pair of arcs with the other intersection point at $Q_{1}$. These two arcs have the same intersection angle.