Find angle a,b,c and d

Angle $a$ ($\angle BAC$) is an angle at the circumference subtended by arc BC. The angle at the center subtended by the same arc BC is $120^\circ$.
The angle at the circumference is half the angle at the center.

$$a = \frac{1}{2} \times 120^\circ$$ $$a = 60^\circ$$

Angle $c$ ($\angle BDC$) is also an angle at the circumference subtended by the same arc BC. Angles subtended by the same arc in the same segment are equal.
Therefore, $c = a$.

$$c = 60^\circ$$

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