Question

the circle below has center \\(h\\). suppose that \\(m \widehat{fg} = 116^{\circ}\\). find the following.

(a) \\(m \angle feg = \box^{\circ}\\)
(b) \\(m \angle fhg = \box^{\circ}\\)

Explanation:

Find the central angle measure

Using the Central Angle knowledge point

$$ m\angle FHG = m\widehat{FG} = 116^\circ $$

Find the inscribed angle measure

Using the Inscribed Angle Theorem knowledge point

$$ m\angle FEG = \frac{1}{2} \cdot m\widehat{FG} = \frac{1}{2} \cdot 116^\circ = 58^\circ $$

Answer:

Question 1

(a) \(m\angle FEG = 58^\circ\)

Question 2

(b) \(m\angle FHG = 116^\circ\)