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Answer:

∠AOB = 120°

∠BOC = 140°

∠BOD = 140°

Step-by-step explanation:

First, find X !

Full circle is 360°

360 = (2x + 80) + (5x + 40) + 4x + x

360 = 12x + 120

240 = 12x

x = 20°

Substitute the X

∠AOB ≡ (2x + 80) =

(2(20) + 80) = 120°

∠BOC ≡ (5x + 40) =

(5(20) + 40) = 140°

∠BOD = ∠AOB + ∠DOA ≡

120 + x = 120 + 20 = 140°

Answer:

Step-by-step explanation:

Lines A , B, C and D meet at a point, O. Different angles are formed at this poin, O.

The sum of the angles at point O is 360 degrees. It means that

x + (2x + 80) + (5x + 40) + 4x = 360 degrees

x + 2x + 80 + 5x + 40 + 4x = 360 .

x + 2x + 4x + 5x + 80 + 40 = 360

12x + 120 = 360

12x = 360 - 120 = 240

x = 240/12 = 20

Therefore

Obtuse angle AOB = 2x + 80 =

2 × 20 + 80 = 120 degrees

Obtuse angle BOC = 5x + 40 = 5 × 20 + 40 = 140 degrees

Obtuse angle BOD = x + 2x + 80 = 20 + 2 × 20 + 80 = 140 degrees

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