Question

Find the given measure

Answer 1

m ∠ GHJ = 60°

Explanation:

Given:

m∠ GFJ = 120°

F is a center of a Circle

FG = FH = FJ = Radii of Same Circle

To Find:

m ∠ GHJ = ?

Solution:

Angle inscribed theorem:

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle i.e 2θ that subtends the same arc on the circle.

m∠ GFJ = center angle = 120°

m ∠ GHJ = Inscribed angle = ?

∴
`m\angle GHJ = (1)/(2)* m\angle GFJ`

∴
`m\angle GHJ = (1)/(2)* 120`

∴
`m\angle GHJ = (120)/(2)`

∴ ∠ GHJ = 60° Final Answer.