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aleksley [76]
3 years ago
14

I need this pls helpp

Mathematics
1 answer:
alexandr1967 [171]3 years ago
3 0

Answer:

m∠7 = 63 degrees

m∠8 = 117 degrees

m∠9 = 63 degrees

Step-by-step explanation:

When two lines intersect at a point, then they formed 2 pairs of vertically opposite angles and 4 pairs of linear angles

  • The vertically opposite angles are equal in measures
  • The linear angles have a sum of 180°

In the given figure

∵ There are two lines intersected at a point

∴ The angle of measure 117° and ∠8 are vertically opposite angles

∴ ∠7 and ∠9 are vertically opposite angles

∴ The angle of measure 117° and ∠7 are linear angles

∵ The vertically opposite angles are equal in measures

∴ The angle of measure 117° and ∠8 are equal in measures

∴ m∠8 = 117°

∵ The sum of the measures of the linear angles is 180°

∴ m∠7 + 117° = 180°

→ Subtract 118 from both sides

∵ m∠7 + 117 - 117 = 180 - 117

∴ m∠7 = 63°

∵ m∠7 = m∠9 ⇒ proved up

∴ m∠9 = 63°

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Step-by-step explanation:

The equation of the circle is:

x^{2} + (y-1)^{2} = 16

After some algebraic and trigonometric handling:

\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1

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x = 4\cdot \cos \left(t+\frac{\pi}{2}  \right)

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