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Mathematics

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4 steps
  1. Identify the given angle and its relationship with angle aa.

    The angle given as 120∘120^\circ is in the position of angle dd. Angles aa and dd are adjacent angles on a straight line, so their sum is 180∘180^\circ.

    a+d=180∘a + d = 180^\circ a+120∘=180∘a + 120^\circ = 180^\circ
  2. Calculate the value of aa.

    a=180∘−120∘a = 180^\circ - 120^\circ a=60∘a = 60^\circ
  3. Identify the relationship between angle bb and angle dd.

    Angles bb and dd are vertically opposite angles. Vertically opposite angles are equal.

    b=db = d b=120∘b = 120^\circ
  4. Identify the relationship between angle cc and angle aa.

    Angles cc and aa are vertically opposite angles. Vertically opposite angles are equal.

    c=ac = a c=60∘c = 60^\circ

    The values are:
    a=60∘a = \boxed{\text{60}^\circ}
    b=120∘b = \boxed{\text{120}^\circ}
    c=60∘c = \boxed{\text{60}^\circ}
    d=120∘d = \boxed{\text{120}^\circ}

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