Answer :
∠ AOQ = 58° (given)
∠ OBQ = 1/2 ∠AOQ (angle in a semicircle)
⇒ ∠ OBQ = 1/2 × 58° = 29°
In Δ BAT,
∠ABQ + ∠BAT + ∠ATB = 180° (Sum of all the angles of a triangle)
⇒ 29° + 90° + ∠ ATB = 180°
⇒ ∠ ATB = 61°
∴ ∠ ATQ = 61°
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