In the given figure, find the measure of each of the angles ∠DOE and ∠EOA.

From the figure,

∠AOB = 90°, ∠BOC = 112°, ∠COD = 86°, ∠DOE = x°, ∠EOA = 3x°

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

∴ ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°

⇒ 90° + 112° + 86° + x° + 3x° = 360°

⇒ 288° + 4x° = 360°

⇒ 4x° = 360° - 288°

⇒ 4x° = 72°

⇒ x° = $\dfrac{72^{\circ}}{4}$

⇒ x° = 18°

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

∠DOE = x° = 18°

∠EOA = 3x° = (3 x 18)° = 54°

∠DOE = 18°, ∠EOA = 54°.