Deoarece A,O,D sunt coliniare =>
=> m(<AOD)=180⁰
m(<AOD)=m(<AOB)+m(<BOC)+m(<COD) =>
=> 180 = 3x + 90 + x => 4x =180 - 90 => 4x = 90 | : 2 => 2x = 45 =>
x = 44⁰60' : 2 => x = 22⁰30' => m(<DOC)=22⁰30'
m(<AOB)=3 * 22⁰30' = 66⁰90' => m(<AOB)=67⁰30'
EF bisectoarea <BOC => m(<BOF)=m(<FOC)=m(<BOC):2 =>
=> m(<BOF)=m(<FOC)=45⁰
m(<FOC)+m(<COD)=m(<FOD)=>
=>m(<FOD)=45⁰+22⁰30'=44⁰60'+22⁰30' =>
=>m(<FOD)= 66⁰90' = 67⁰30'
Unghiurile <AOE si <FOD sunt opuse la varf:
m(<FOD)=m(<AOE)=67⁰30'
m(<BOE)=m(<AOB)+m(<AOE) => m(<BOE)=2 * 67⁰30' =>
=> m(<BOE)= 134⁰60' = 135⁰
m(<AOF)=m(<AOB)+m(<BOF) = 67⁰30' + 45⁰ =>
=> m(<AOF)= 112⁰30'
Unghiurile <AOF si <DOE sunt opuse la varf:
m(<DOE)=m(<AOF)=112⁰30'
