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A circle contains 360 degrees. Draw a circle, add a radius to any point on it, and then rotate the radius completely around. After it has returned to the point it initially intersected the curve, the radius will have rotated through 360 degrees.(another explanation, maybe no better.)A complete circle measures 360 degrees, so a half-circle is 180 degrees, a quarter-circle is 90 degrees and so forth. Another way to look at it is in terms of the central angle formed by the radii drawn from each endpoint of the arc - the measure of the arc in degrees is the same as the measure of this central angle in degrees.
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A circle is 360 degrees if that's what you're asking.
A semi-circle, half a circle, by definition is 180 degrees, half of a rotation. A whole circle has a whole rotation, which is 360 degrees.
-- The major arc = 230 degrees-- The minor arc ... the arc between the tangents ... is (360 - 230) = 130 degrees.-- The line from the vertex of the angle to the center of the circle bisects the arc,so the angle between that line and the radius to each tangent is 65 degrees.-- The radius to each tangent is perpendicular to the tangent. So the radius, the tangent,and the line from the vertex to the center of the circle is a right triangle.-- In the right triangle, there's 90 degrees where the radius meets the tangent, and65 degrees at the center of the circle. That leaves 25 degrees for the angle at thevertex.-- With another 25 degrees for the right triangle formed by the other tangent,the total angle formed by the two tangents is 50 degrees.