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In the given figure, find the values of d and e.

Mathematics

ScanSolve AI Answer

Answer

d=55∘d = 55^\circ

e=28∘e = 28^\circ

Step-by-step solution

4 steps
  1. Identify angles subtended by the same arc.

    The angle 55∘55^\circ is ∠CAD\angle CAD. This angle is subtended by arc CD.
    The angle dd is ∠CBD\angle CBD. This angle is also subtended by arc CD.

  2. Apply the theorem that angles subtended by the same arc at the circumference are equal.

    Since ∠CAD\angle CAD and ∠CBD\angle CBD both subtend arc CD, their measures are equal.

    d=55∘d = 55^\circ
  3. Identify another pair of angles subtended by the same arc.

    The angle 28∘28^\circ is ∠BCA\angle BCA. This angle is subtended by arc AB.
    The angle ee is ∠ADB\angle ADB. This angle is also subtended by arc AB.

  4. Apply the theorem that angles subtended by the same arc at the circumference are equal.

    Since ∠BCA\angle BCA and ∠ADB\angle ADB both subtend arc AB, their measures are equal.

    e=28∘e = 28^\circ

    The values of dd and ee are:

    d=55∘d = \boxed{55^\circ} e=28∘e = \boxed{28^\circ}
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