Question

What is the measure of arc bc? A. 76 B. 40 C. 96 D. 58

Answer 1

Answer:

  A.  76

Step-by-step explanation:

Angle A is half the difference between the measures of arc DE and BC.

  m∠A = (1/2)(DE -BC)

  20 = (1/2)(116 -BC) . . . . substitute the given values

  40 = 116 -BC . . . . . . . . multiply by 2

  BC = 116 -40 . . . . . . . . add BC -40

  BC = 76

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Comment on intersecting secants

When the secants intersect inside the circle, the angle where they cross is half the sum of the intercepted arcs. When they intersect outside the circle (as here), the angle where they meet is half the difference of the intercepted acs.

Sometimes it is easier to remember two related relationships than it is to remember just one of them.