Answer:
The measure of the four angles are 30°, 60°, 120°, 150°
Step-by-step explanation:
Q 11.
The sum of the measures of the angle at a point is 360°
Let us use this fact to answer the question
→ Assume that m∠AOB is x°
∵ m∠AOB = x°
∵ m∠BOC is twice m∠AOB
∴ m∠BOC = 2x°
∵ m∠COD is 4 times m∠AOB
∴ m∠COD = 4x°
∵ m∠DOA is 5 times m∠AOB
∴ m∠DOA = 5x°
→ By using the fact above
∵ m∠AOB + m∠BOC + m∠COD + m∠DOA = 360°
∴ x° + 2x° + 4x° + 5x° = 360°
→ Add the like terms
∴ 12x° = 360°
→ Divide both sides by 12
∴ x = 30°
→ Substitute the value of x in each angle to find them
∵ m∠AOB = x°
∴ m∠AOB = 30°
∵ m∠BOC = 2x° = 2(30°)
∴ m∠BOC = 60°
∵ m∠COD = 4x° = 4(30°)
∴ m∠COD = 120°
∵ m∠DOA = 5x° = 5(30)
∴ m∠DOA = 150°
∴ The measure of the four angles are 30°, 60°, 120°, 150°
