In the given figure, AOB is a straight line. If ∠BOC, ∠COD and ∠DOA be in the ratio 2 : 3 : 4, find the measure of each of these angles.

Given:

∠BOC = (2x)°

∠COD = (3x)°

∠DOA = (4x)°

Since, AOB is a straight line,

∴ ∠BOC + ∠COD + ∠DOA = 180°

Substituting the values in above, we get:

2x° + 3x° + 4x° = 180°

⇒ 9x° = 180°

⇒ x° = $\dfrac{180^{\circ}}{9}$

⇒ x° = 20°

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

∠BOC = (2x)° = (2 x 20)° = 40°

∠COD = (3x)° = (3 x 20)° = 60°

∠DOA = (4x)° = (4 x 20)° = 80°

∠BOC = 40°, ∠COD = 60° and ∠DOA = 80°.