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

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

KnowledgeBoat · Accepted Answer

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° = ⇒ 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°.

Mathematics

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

Lines & Angles

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