HMMT November 2024 H6

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Let $F E L D S P A R$ be a regular octagon, and let $I$ be a point in its interior such that $\angle F I L=\angle L I D=$ $\angle D I S=\angle S I A$ . Compute $\angle I A R$ in degrees.

Dataset text NuminaMath olympiads. Quoted with source.

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82.5^{\circ}

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