Answer:
a = 49°
Step-by-step explanation:
From the figure attached,
In ΔBOC,
OB = OC = Radii of the circle O
Therefore, m∠OBC = m∠OCB = 41° [Opposite angles of the equal sides of a triangle]
By triangle sum theorem,
m∠OBC + m∠OCB + m∠BOC = 180°
41° + 41° + m∠BOC = 180°
m∠BOC = 180° - 82°
= 98°
Since, "angle subtended by an arc at the center is twice the angle subtended at the circumference",
m∠BOC = 2(m∠BAC)
98° = 2(a)
a = 49°
