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Given m < AFB = 40, m < BAF = 90, and m < AGD = 86. Find measure of arc AC.

Given m < AFB = 40, m < BAF = 90, and m < AGD = 86. Find measure of arc AC-example-1

1 Answer

5 votes

Answer: 100 degrees

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Step-by-step explanation:

Refer to the figure below.

Focus on triangle ABF. Angle AFB = 40 is marked in red. Angle BAF = 90 is marked in blue. The missing angle is 180-90-40 = 50 which is angle ABF.

Inscribed angle ABF = 50 doubles to arc AC since this inscribed angle subtends the arc in question. I'm using the inscribed angle theorem.

arc AC = 2*(angle ABF) = 2*50 = 100 degrees

Note: We don't need the fact that angle AGD = 86

Given m < AFB = 40, m < BAF = 90, and m < AGD = 86. Find measure of arc AC-example-1
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