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3 years ago

Do Q11 do carefully step by step

Mathematics

1 answer:

azamat3 years ago

7 0

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°

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Given tangent, ZN, to the circle and the arc $\widehat{ZMB}$ = 280°, we have that

the angle formed by the chord BZ and the tangent ZN, ∠BZN is 50°

<h3>Which method can be used to find ∠BZN?</h3>

The given parameters are;

A tangent to the circle O = ZN

$m \widehat{ZMB}} = \mathbf{280^{\circ}}$

Required:

Angle ∠BZN

Solution;

Please find attached the drawing of the circle and tangent

From the drawing, we have;

∠BOZ = 360° - 280° = 80°

ΔBOZ is an isosceles triangle, which gives;

∠BZO = ∠ZBO

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∠OZN = 90° (by definition of a tangent)

∠OZN = ∠BZO + ∠BZN

∠BZN = ∠OZN - ∠BZO

Which gives;

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The measure of angle ∠BZN =<u> 50°</u>

Learn more about tangents to a circle here:

brainly.com/question/14561226

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3 years ago