In the given figure, find the measure of each of the angles ∠AOB, ∠BOC, ∠COD and ∠DOA.

From the figure,

∠AOB = x°, ∠BOC = 2x°, ∠COD = 3x°, ∠DOA = 4x°

At point O, all angles around a point add up to 360°

∴ ∠AOB + ∠BOC + ∠COD + ∠DOA = 360°

⇒ x° + 2x° + 3x° + 4x° = 360°

⇒ 10x° = 360°

⇒ x° = $\dfrac{360^{\circ}}{10}$

⇒ x° = 36°

Let's find the measure of each angle by substituting the value of x:

∠AOB = x° = 36°

∠BOC = 2x° = (2 x 36)° = 72°

∠COD = 3x° = (3 x 36)° = 108°

∠DOA = 4x° = (4 x 36)° = 144°

∠AOB = 36°, ∠BOC = 72°, ∠COD = 108° and ∠DOA = 144°.