Question

Determine mABDarc using the appropriate theorems and postulates.

Answer 1

Answer: 56 degrees

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Work Shown:

Given Info

arc BCD = 21

arc EF = 35 (this is the shortest distance along the circle from points E to F)

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Using arc EF, we can say that angle ECF is also the same measure. The central angle and the arc measure are always equal.

angle ECF = 35

Then using the vertical angle theorem, we can say that

angle ACB = angle ECF

angle ACB = 35

From the fact that central angle ACB is 35 degrees, we can then say minor arc AB is also 35 degrees

Through similar reasoning, minor arc BD = angle BCD = 21

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So we have

• minor arc AB = 21
• minor arc BD = 35

which add to

(minor arc AB)+(minor arc BD) = arc ABD

(21)+(35) = arc ABD

56 = arc ABD

arc ABD = 56

See the diagram below and hopefully it will clear up any confusion. The diagram is composed of two figures. Figure 1 shows how to get minor arc AB. Figure 2 shows how to get minor arc BD.