Question

in the figure below, points g, h, and j all lie on circle i.
which of the following can be concluded from the figure?

• ( mangle jih = \frac{1}{3}mangle jgh )
• ( mangle jgh = \frac{1}{3}mangle jih )
• ( mangle jgh = \frac{1}{2}mangle jih )
• ( mangle jih = \frac{1}{2}mangle jgh )

Explanation:

To solve this, we use the inscribed angle theorem. The central angle \( \angle JIH \) subtends arc \( JH \), and the inscribed angle \( \angle JGH \) also subtends arc \( JH \). The theorem states that an inscribed angle is half the measure of its subtended central angle. So \( m\angle JGH=\frac{1}{2}m\angle JIH \).

Answer:

\( m\angle JGH = \frac{1}{2}m\angle JIH \) (the option with this expression)