Question

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

Answer 1

9514 1404 393

Answer:

  a.  x = 60

  b.  y = 93

Step-by-step 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°

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Using these relations, we have ...

  A = (BC -x°)/2

  x° = BC -2A = 114° -2(27°)

  x° = 60°

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

  y° = 93°