CIRCLES C8

In the figure below, find the value of <FGE.

Solution

<FEG = <HFG

∴ <FEG = 54⁰ [angles in alternate segments are equal.]

Consider ∆GEF

<EFG + <FGE+ <GEF = 180⁰ [total degrees of a triangle]

 (39⁰ + 54⁰) + <FGE + 54= 180⁰

93⁰ + <FGE + 54⁰ = 180⁰

147⁰ + <FGE= 180⁰

<FGE= 180⁰ - 147⁰

<FGE= 33⁰  

∴ <FGE = 33⁰