Find angle a,b,c and d

Step 1: Find angle $a$. 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. $a = \frac{1}{2} \times 120^\circ$ $a = 60^\circ$

Step 2: Find angle $c$. 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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