Do Q1, Q2 all parts do carefully step by step

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°

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step-by-step explanation: