In the adjoining figures, find angle AOC = (2y-13)° and angle BOC=(3y-12)°, find all the four angles
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Given :- In the adjoining figures, find angle AOC = (2y-13)° and angle BOC=(3y-12)°, find all the four angles ?
Solution :-
we have ,
- ∠AOC = (2y - 13)°
- ∠BOC = (3y - 12)°
So,
→ ∠AOC + ∠BOC = 180° (linear pair)
→ (2y - 13) + (3y - 12) = 180°
→ 2y + 3y - 13 - 12 = 180°
→ 5y - 25 = 180°
→ 5(y - 5) = 180°
→ y - 5 = 36°
→ y = 36 + 5
→ y = 41° .
Then,
- ∠AOC = 2*41 - 13 = 82 - 13 = 69° .
- ∠BOC = 3*41 - 12 = 123 - 12 = 111° .
Therefore, by vertically opposite angles ,
- ∠AOC = ∠BOD
- ∠BOC = ∠AOD
Hence, all four angles are :-
- ∠AOC = 69°
- ∠BOC = 111°
- ∠BOD = 69°
- ∠AOD = 111° .
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