Question

question
given circle f with chords \\( \overline { g h }, \overline { h k }, \overline { j g }, \overline { g k }, \overline { j i } \\), and \\( \overline { g i } \\). \\( \overline { g h } \cong \overline { g i } \\). name an angle congruent to \\( \angle g j i \\).

Explanation:

Step1: Recall the Inscribed Angle Theorem

In a circle, congruent chords subtend congruent arcs. Since \( \overline{GH}\cong\overline{GI}\), the arc \( \overset{\frown}{GH}\cong\overset{\frown}{GI}\).

Step2: Use the property of inscribed angles

The measure of an inscribed angle is half the measure of its subtended arc. \(\angle GJI\) subtends arc \(\overset{\frown}{GI}\), and \(\angle GHI\) subtends arc \(\overset{\frown}{GH}\).

Answer:

\(\angle GHI\)