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AB is tangent to the circle at B. M∠A = 27 and mBC=114 (The figure is not drawn to scale.)

AB is tangent to the circle at B. M∠A = 27 and mBC=114 (The figure is not drawn to-example-1

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Answer:

a. x = 60

b. y = 93

Explanation:

The relevant relations are ...

  • external angle A is half the difference of intercepted arcs BC and BD
  • inscribed angle y° is half the measure of intercepted arc CD
  • the sum of arcs of a circle is 360°

__

Using these relations, we have ...

A = (BC -x°)/2

x° = BC -2A = 114° -2(27°)

x° = 60°

__

y° = CD/2 = (360° -BC -BD)/2 = (360° -114° -60°)/2

y° = 93°

AB is tangent to the circle at B. M∠A = 27 and mBC=114 (The figure is not drawn to-example-1
User Oillio
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