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An arc is a smooth piece of a circle. A major arc of a circle is an arc that is longer than half the circumference of the circle. Find the measure of the major arc ABC.

Part I: The mŁABC is equal to one half of the mac. (Circle one) (1 point)

Part II: Using the relationship you established in Part I, find the mac. Show your work and explain
your answer. (2 points)

Part III: Using your answer from Part II, find the mABC. Show your work. (2 points)

An arc is a smooth piece of a circle A major arc of a circle is an arc that is longer than half the circumference of the circle Find the measure of the major ar class=

Respuesta :

Part 1

Answer: one half

The angle ABC is one half of minor arc AC

Explanation: A minor arc is any arc that has measure less than 180 degrees (ie smaller than half the circle). Due to the inscribed angle theorem, any inscribed angle is always one half of the arc it cuts off

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Part 2

Answer: 80 degrees

Explanation: Angle ABC is 40 degrees as shown in the diagram. Minor arc AC is 80 degrees since the inscribed angle is half of the arc. Put another way, the arc is twice that of the inscribed angle. This is something you should put in your notebook or on a reference card

  • inscribed angle = (1/2)*arc
  • arc = 2*(inscribed angle)

So we can say

minor arc AC = 2*(inscribed angle)

minor arc AC = 2*40

minor arc AC = 80 degrees

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Part 3

Answer:  280 degrees.

Explanation: Major arc ABC and minor arc AC combine to get the full circle of 360 degrees. We know minor arc AC is 80 degrees, so 360-80 = 280 is the remaining bit.

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