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Ostrovityanka [42]
3 years ago
9

unghiurile ∢AOB și ∢COD sunt unghiuri opuse la vârf, O ∈ AC, iar PO ⊥ BD, P∈ Int ∢AOD. Dacă ∢COP = 133°, aflați măsurile unghiur

ilor ∢AOB și ∢BOC.

Mathematics
1 answer:
lbvjy [14]3 years ago
8 0

Răspuns:

<AOB = 43 ° și <BOC = 137 °

Explicație pas cu pas:

Găsiți diagrama atașată pentru o mai bună explicație a întrebării.

Din diagramă, <COP = <DOP + <COD

Deoarece <DOP = 90 ° și <COP = 133 °, la înlocuire

133 ° = 90 ° + <COD

<COD = 133 ° -90 °

<COD = 43 °

Deoarece <COD = <AOB (unghiuri direcționate opuse), deci <AOB = 43 °

Pentru <BOC:

Suma unghiurilor pe DBO dreaptă este de 180 °.

<BOC + <COD = 180 °

Dat <COD = 43 °

<BOC + 43 = 180 °

<BOC = 180 ° -43 °

<BOC = 137 °

Prin urmare, <AOB = 43 ° și <BOC = 137 °

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