Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle.

Question

Mathematics

Emilio Winters

31 January, 12:56

Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle.

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Answers (2)

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Triston Harding · Answer 1

Prove:

The angle inscribed in a semicircle is a right angle.

The inscribed angle theorem states that the angle θ, inscribed in a circle is half the measure of the central angle of the circle. So, if the given is a semi-circle, then the inscribed angle is half of 180, therefore, 90 degrees and a right angle.

Lincoln Dorsey · Answer 2

A circle measures 360 degrees, so a semicircle measures 180 degrees. By using the inscribed angle theorem, the measure of the inscribed angle would be half of 180 degrees, or 90 degrees, which is a right angle.

That's the right answer I got.