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

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° $\quad$[Grouping like terms]

⇒ 10x° + 10° = 360°

⇒ 10x° = 360° - 10°

⇒ 10x° = 350°

⇒ x° = $\dfrac{350^{\circ}}{10}$

⇒ 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°.