Question

[100 POINTS] What is the measure of the arc from A to B that does not pass through C?

Answer 1

Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.

What is the Inscribed Angle Theorem?

Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).

m∠BAC = 40 degrees.

Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]

Corresponding arc BC = 80 degrees.

Arc AC through point B = 180 degrees [half circle]

Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.

Learn more about the inscribed angle theorem on:

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