Find the inscribed angle resting on an arc that is 1/4 of the circle.
| May 2, 2021 | education
The inscribed angle is the angle, the vertex of which lies on the circle, and all its sides intersect it.
The degree measure of the inscribed angle is equal to half of the degree measure of the arc on which it rests:
∠ABS = UAC / 2.
Since the degree measure of the arc of a circle is equal to the degree measure of the central angle that rests on it, and the sum of the degree measures of all central angles is 360 degrees, then:
UАС = 360º · 1/4 = 90º.
∠ABS = 90º / 2 = 45º.
Answer: the degree measure of the inscribed angle ∠АВС is equal to 45º.
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