1. Given an inscribed circle with chords EF, FH, HG, and GE intersecting at O, and the angle \(\angle EOH = 53^\circ\), find \(\angle EFHI\). 2. The problem states that \(\angle EOH = 53^\circ\). Since chords EF and HG intersect at O, the angle formed between these chords inside the circle is half the sum of the arcs intercepted by these chords. 3. Using the intersecting chords theorem: \(\angle EOH = \frac{1}{2}(\text{arc } EH + \text{arc } FG)\). Given \(\angle EOH = 53^\circ\), we can find \(\angle EFHI\) which is the angle subtended by chord FH at the circumference. 4. The angle subtended by chord FH at the circumference \(\angle EFHI\) is half the measure of the intercepted arc EH, so \(\angle EFHI = \frac{1}{2} \times 53^\circ = 26.5^\circ\). Final answer: \(\boxed{26.5^\circ}\)