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14 March, 04:35

Which angles intercept a 20 degree arc in a circle? Select all that apply.

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  1. 14 March, 04:42
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    b. A central angle of 20 degrees

    d. An inscribed angle of 10 degrees

    Step-by-step explanation:

    The complete question is

    Which angles intercept a 20 degree arc in a circle? Select all that apply.

    a. A central angle of 10 degrees

    b. A central angle of 20 degrees

    c. A central angle of 40 degrees

    d. An inscribed angle of 10 degrees

    e. An inscribed angle of 20 degrees

    f. An inscribed angle of 40 degrees

    Verify each case

    case a. A central angle of 10 degrees

    we know that

    Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it'

    so

    A central angle of 10 degrees, intercept a 10 degree arc in a circle (by central angle)

    case b. A central angle of 20 degrees

    we know that

    Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it'

    so

    A central angle of 20 degrees, intercept a 20 degree arc in a circle (by central angle)

    case c. A central angle of 40 degrees

    we know that

    Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it'

    so

    A central angle of 40 degrees, intercept a 40 degree arc in a circle (by central angle)

    case d. An inscribed angle of 10 degrees

    we know that

    The inscribed angle is half that of the arc it comprises

    so

    An inscribed angle of 10 degrees, intercept a 20 degree arc in a circle

    case e. An inscribed angle of 20 degrees

    we know that

    The inscribed angle is half that of the arc it comprises

    so

    An inscribed angle of 20 degrees, intercept a 40 degree arc in a circle

    case f. An inscribed angle of 40 degrees

    we know that

    The inscribed angle is half that of the arc it comprises

    so

    An inscribed angle of 40 degrees, intercept a 80 degree arc in a circle
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