I need help with these two questions and can you please explain how you got the answer?

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  • Alan
    Lv 7
    6 months ago
    Favorite Answer

    Exterior Angle Rule

    <ex angle = 1/2( outer arc - inner arc)

    therefore

    if arc are measured clockwise

    <Angle A= 1/2 ( arc BC (from B to C) - arc RS (from S to R) )

    36 = 1/2 ( arc BC - (1/4) arc BC) =

    36= 1/2 BC - 1/8 BC = BC(4/8 -1/8) = (3/8) Arc BC

    multiply both sides by 8/3

    36*(8/3) = arc BC

    arc BC = 96

    arc RS = 96/4= 24 degrees

    checking

    36= (1/2)(96-24) = 1/2 (72) =36

    37.

    so AB is the side of a triangle with sides PA and PB.

    All sides of equal.

    Meaning it is an equilateral triangle

    <P = 60 degrees (if you measured the shorter angle)

    which would be 360-60 =300 degrees if you measure the other way.

    alternatively

    chord length formula

    C = 2r*sin(theta/2)

    so if r = C,

    C/2C = sin(theta/2)

    1/2 = sin(theta/2)

    arcsin(1/2) = 30 or 150 = theta/2

    theta = 2*30 or 2*150 = 60 or 300

    again if you measure only the shorter angle = 60 degrees.

    if you measure the wider angle it is 300 degrees.

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