The angle at the apex of an isosceles triangle is 100 degrees. Find the degrees of magnitude of the arcs into which the vertices of this triangle divide the circumscribed circle.
The inscribed angle ABC, by condition, is equal to 100, then the degree measure of the arc AC = 2 * 100 = 200.
Since the triangle ABC is isosceles, the angle BAC = BCA = (180 – ABC) / 2 = (180 – 100) / 2 = 80/2 = 40.
The inscribed angle BAC rests on the arc BC, the degree measure of which is equal to two values of the inscribed angle. Arc BC = 2 * 40 = 80.
Since the inscribed angle BCA = BAC, then the degree measure of the arc AB = BC = 80.
Answer: The degree measures of the arcs are 200, 80, 80.
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