Question

In the adjoining figures, find angle AOC = (2y-13)° and angle BOC=(3y-12)°, find all the four angles

Answer 1

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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