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

Question

KnowledgeBoat · Accepted Answer

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° = ⇒ 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°.

Mathematics

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

Lines & Angles

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