In the given figure, find the value of x. What is the measure of ∠COD?

Question

KnowledgeBoat · Accepted Answer

From the figure, ∠AOB = (x - 5)°, ∠BOC = (2x - 5)°, ∠COD = (3x + 20)°, ∠DOA = 4x° At point O, all angles around a point add up to 360° ∴ ∠AOB + ∠BOC + ∠COD + ∠DOA = 360° ⇒ (x - 5)° + (2x - 5)° + (3x + 20)° + 4x° = 360° ⇒ x° + 2x° + 3x° + 4x° - 5° - 5° + 20° = 360° [Grouping like terms] ⇒ 10x° + 10° = 360° ⇒ 10x° = 360° - 10° ⇒ 10x° = 350° ⇒ x° = ⇒ x° = 35° Let's find ∠COD by substituting the value of x: ∠COD = (3x + 20)° = (3(35) + 20)° = (105 + 20)° = 125° The value of x° is 35°, and the measure of ∠COD is 125°.

Mathematics

In the given figure, find the value of x. What is the measure of ∠COD?

Lines & Angles

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